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Journal articles on the topic 'Left-commutative algebras'

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Published: 3 June 2025
Last updated: 31 July 2025

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1

Lee, Jeong-Gon, Ravikumar Bandaru, Kul Hur, and Young Bae Jun. "Interior GE-Algebras." Journal of Mathematics 2021 (February 5, 2021): 1–10. http://dx.doi.org/10.1155/2021/6646091.

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The concepts of (commutative, transitive, left exchangeable, belligerent, antisymmetric) interior GE-algebras and bordered interior GE-algebras are introduced, and their relations and properties are investigated. Many examples are given to support these concepts. A semigroup is formed using the set of interior GE-algebras. An example is given that the set of interior GE-algebras is not a GE-algebra. It is clear that if X is a transitive (resp., commutative, belligerent, and left exchangeable) GE-algebra, then the interior GE-algebra X , f is transitive (resp., commutative, belligerent, and lef
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2

Li, Guo, and Zheng Shanghua. "Left counital Hopf algebra structures on free commutative Nijenhuis algebras." SCIENTIA SINICA Mathematica 50, no. 6 (2019): 829. http://dx.doi.org/10.1360/scm-2017-0662.

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3

Gorshkov, Ilya, Ivan Kaygorodov, and Yury Popov. "Degenerations of Jordan Algebras and “Marginal” Algebras." Algebra Colloquium 28, no. 02 (2021): 281–94. http://dx.doi.org/10.1142/s1005386721000225.

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We describe all degenerations of the variety [Formula: see text] of Jordan algebras of dimension three over [Formula: see text]. In particular, we describe all irreducible components in [Formula: see text]. For every [Formula: see text] we define an [Formula: see text]-dimensional rigid “marginal” Jordan algebra of level one. Moreover, we discuss marginal algebras in associative, alternative, left alternative, non-commutative Jordan, Leibniz and anticommutative cases.
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4

Spiegel, Eugene. "Essential ideals of incidence algebras." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 2 (2000): 252–60. http://dx.doi.org/10.1017/s1446788700001981.

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AbstractIt is determined when there exists a minimal essential ideal, or minimal essential left ideal, in the incidence algebra of a locally finite partially ordered set defined over a commutative ring. When such an ideal exists, it is described.
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5

Runde, Volker. "A functorial approach to weak amenability for commutative Banach algebras." Glasgow Mathematical Journal 34, no. 2 (1992): 241–51. http://dx.doi.org/10.1017/s0017089500008788.

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Let A be a commutative algebra, and let M be a bimodule over A. A derivation from A into M is a linear mapping D: A→M that satisfiesIf M is only a left A-module, by a derivation from A into M we mean a linear mapping D: A→M such thatEach A-bimodule M is trivially a left module. However, unless it is commutative, i.e.the two classes of linear operators from A into M characterized by (1) and (2), respectively, need not coincide.
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6

Dvurečenskij, Anatolij. "Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras." Journal of the Australian Mathematical Society 74, no. 1 (2003): 121–44. http://dx.doi.org/10.1017/s1446788700003177.

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AbstractPseudo-effect algebras are partial algebras (E; +, 0, 1) with a partially defined addition + which is not necessary commutative and with two complements, left and right ones. We define central elements of a pseudo-effect algebra and the centre, which in the case of MV-algebras coincides with the set of Boolean elements and in the case of effect algebras with the Riesz decomposition property central elements are only characteristic elements. If E satisfies general comparability, then E is a pseudo MV-algebra. Finally, we apply central elements to obtain a variation of the Cantor-Bernste
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7

LYKOVA, ZINAIDA A. "Relations between the homologies of C*-algebras and their commutative C*-subalgebras." Mathematical Proceedings of the Cambridge Philosophical Society 132, no. 1 (2002): 155–68. http://dx.doi.org/10.1017/s0305004101005497.

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The paper concerns the identification of projective closed ideals of C*-algebras. We prove that, if a C*-algebra has the property that every closed left ideal is projective, then the same is true for all its commutative C*-subalgebras. Further, we say a Banach algebra A is hereditarily projective if every closed left ideal of A is projective. As a corollary of the stated result we show that no infinite-dimensional AW*-algebra is hereditarily projective. We also prove that, for a commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space, the following conditions are
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8

KOLOGANI, MONA AALY, MOHAMMAD MOHSENI TAKALLO, RAJAB ALI BORZOOEI, and YOUNG BAE JUN. "Right and Left Mappings in Equality Algebras." Kragujevac Journal of Mathematics 46, no. 5 (2022): 815. http://dx.doi.org/10.46793/kgjmat2205.815k.

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The notion of (right) left mapping on equality algebras is introduced, and related properties are investigated. In order for the kernel of (right) left mapping to be filter, we investigate what conditions are required. Relations between left mapping and →-endomorphism are investigated. Using left mapping and →-endomorphism, a characterization of positive implicative equality algebra is established. By using the notion of left mapping, we define →-endomorphism and prove that the set of all →-endomorphisms on equality algebra is a commutative semigroup with zero element. Also, we show that the set
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9

Altayeva, A. B., and B. Sh Kulpeshov. "Algebras of Binary Formulas for Weakly Circularly Minimal Theories: Monotonic-to-left Case." Bulletin of Irkutsk State University. Series Mathematics 52 (2025): 120–36. https://doi.org/10.26516/1997-7670.2025.52.120.

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This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. Algebras of binary isolating formulas are studied for ℵ0-categorical 1-transitive non-primitive weakly circularly minimal theories of convexity rank greater than 1 with a trivial definable closure having a non-trivial monotonic-to-left function acting on the universe of a structure. On the basis of the study, the authors present a description of these algebras. It is shown that for this case there exist only non-commutative algebras. A strict m-deterministicity of suc
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10

Singh, Surjeet, and Fawzi Al-Thukair. "Some chain conditions on weak incidence algebras." International Journal of Mathematics and Mathematical Sciences 2005, no. 15 (2005): 2389–97. http://dx.doi.org/10.1155/ijmms.2005.2389.

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LetXbe any partially ordered set,Rany commutative ring, andT=I∗(X,R)the weak incidence algebra ofXoverR. LetZbe a finite nonempty subset ofX,L(Z)={x∈X:x≤z for some z∈Z}, andM=Tez. Various chain conditions onMare investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.
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11

Wardati, K. "The socle of Leavitt path algebras over a semiprime ring." Algebra and Discrete Mathematics 34, no. 1 (2022): 152–68. http://dx.doi.org/10.12958/adm1850.

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The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points.
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12

JANSSEN, K., and J. VERCRUYSSE. "MULTIPLIER BI- AND HOPF ALGEBRAS." Journal of Algebra and Its Applications 09, no. 02 (2010): 275–303. http://dx.doi.org/10.1142/s0219498810003926.

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We propose a categorical interpretation of multiplier Hopf algebras, in analogy to usual Hopf algebras and bialgebras. Since the introduction of multiplier Hopf algebras by Van Daele [Multiplier Hopf algebras, Trans. Amer. Math. Soc.342(2) (1994) 917–932] such a categorical interpretation has been missing. We show that a multiplier Hopf algebra can be understood as a coalgebra with antipode in a certain monoidal category of algebras. We show that a (possibly nonunital, idempotent, nondegenerate, k-projective) algebra over a commutative ring k is a multiplier bialgebra if and only if the catego
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13

Romano, Daniel A. "Pseudo Quasi-Ordered Residuated Systems, An Introduction." Pan-American Journal of Mathematics 1 (August 23, 2022): 12. http://dx.doi.org/10.28919/cpr-pajm/1-12.

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The concept of quasi-ordered residuated systems was introduced in 2018 by S. Bonzio and I. Chajda as a generalization of both hoop-algebras and commutative residuated lattices ordered by quasi-orders. The substructures of ideals and filters in such algebraic structures were considered by the author. This paper introduces and analyzes the concept of pseudo quasi-ordered residuated systems as a non-commutative generalization of quasi-ordered residuated systems with left and right residuum operations. Also, this paper discusses the concepts of ideals and filters in pseudo quasi-ordered residuated
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14

ASCHIERI, PAOLO. "TWISTING ALL THE WAY: FROM ALGEBRAS TO MORPHISMS AND CONNECTIONS." International Journal of Modern Physics: Conference Series 13 (January 2012): 1–19. http://dx.doi.org/10.1142/s201019451200668x.

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Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules [Formula: see text], where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist [Formula: see text] of H we then quantize (deform) H to [Formula: see text], A to A⋆ and correspondingly the category [Formula: see text] to [Formula: see text]. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphism
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15

Moldovyan, Alexandr, and Nikolay Moldovyan. "New Forms of Defining the Hidden Discrete Logarithm Problem." SPIIRAS Proceedings 18, no. 2 (2019): 504–29. http://dx.doi.org/10.15622/sp.18.2.504-529.

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There are introduced novel variants of defining the discrete logarithm problem in a hidden group, which represents interest for constructing post-quantum cryptographic protocols and algorithms. This problem is formulated over finite associative algebras with non-commutative multiplication operation. In the known variant this problem, called congruent logarithm, is formulated as superposition of exponentiation operation and automorphic mapping of the algebra that is a finite non-commutative ring. Earlier it has been shown that congruent logarithm problem defined in the finite quaternion algebra
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16

Saorín, Manuel. "Monoid gradings on algebras and the cartan determinant conjecture." Proceedings of the Edinburgh Mathematical Society 41, no. 3 (1998): 539–51. http://dx.doi.org/10.1017/s0013091500019878.

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In this work we tackle the Cartan determinant conjecture for finite-dimensional algebras through monoid gradings. Given an adequate ∑-grading on the left Artinian ring A, where ∑ is a monoid, we construct a generalized Cartan matrix with entries in ℤ∑, which is right invertitale whenever gl.dim A < ∞. That gives a positive answer to the conjecture when A admits a strongly adequate grading by an aperiodic commutative monoid. We then show that, even though this does not give a definite answer to the conjecture, it strictly widens the class of known graded algebras for which it is true.
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17

Schrempf, Konrad. "A standard form in (some) free fields: How to construct minimal linear representations." Open Mathematics 18, no. 1 (2020): 1365–86. http://dx.doi.org/10.1515/math-2020-0076.

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Abstract We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra techniques for the construction of minimal linear representations (in standard form) for the sum and the product of two elements (given in a standard form). This completes “minimal” arithmetic in free fields since “minimal” constructions for the inverse are already known. The applications are wide: linear algebra (over the free field), ra
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18

Kadioglu, Hulya. "A computational approach for the classifications of all possible derivations of nilsolitons in dimension 9." Thermal Science 26, Spec. issue 2 (2022): 759–83. http://dx.doi.org/10.2298/tsci22s2759k.

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In mathematics and engineering, a manifold is a topological space that locally resembles Euclidean space near each point. Defining the best metric for these manifolds have several engineering and science implications from controls to optimization for generalized inner product applications of Gram Matrices that appear in these applications. These smooth geometric manifold applications can be formalized by Lie Groups and their Lie Algebras on its infinitesimal elements. Nilpotent matrices that are matrices with zero power with left-invariant metric on Lie group with non-commutative properties na
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19

LIU, CHENG-KAI. "AN ENGEL CONDITION WITH AUTOMORPHISMS FOR LEFT IDEALS." Journal of Algebra and Its Applications 13, no. 02 (2013): 1350092. http://dx.doi.org/10.1142/s0219498813500928.

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Let R be a prime ring and L a nonzero left ideal of R. For x, y ∈ R, we denote [x, y] = xy-yx the commutator of x and y. In this paper, we prove that if R admits a non-identity automorphism σ such that [[…[[σ(xn0), xn1], xn2], …], xnk] = 0 for all x ∈ L, where n0, n1, n2, …, nk are fixed positive integers, then R is commutative. The analogous results for semiprime rings and von Neumann algebras are also obtained.
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20

Sanghare, Mamadou. "Subrings of I-rings and S-rings." International Journal of Mathematics and Mathematical Sciences 20, no. 4 (1997): 825–27. http://dx.doi.org/10.1155/s0161171297001130.

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LetRbe a non-commutative associative ring with unity1≠0, a leftR-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism ofMis an automorphism ofM. It is well known that every Artinian (resp. Noetherian) module satisfies property (I) (resp. (S)) and that the converse is not true. A ringRis called a left I-ring (resp. S-ring) if every leftR-module with property (I) (resp. (S)) is Artinian (resp. Noetherian). It is known that a subringBof a left I-ring (resp. S-ring)Ris not in general a left I-ring (resp. S-ring) even ifRis a finitely generatedB-modu
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21

BRZEZIŃSKI, TOMASZ. "DIVERGENCES ON PROJECTIVE MODULES AND NON-COMMUTATIVE INTEGRALS." International Journal of Geometric Methods in Modern Physics 08, no. 04 (2011): 885–96. http://dx.doi.org/10.1142/s0219887811005440.

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A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first-order differential calculus on such a module which admits a hom-connection or a divergence. Properties of integrals associated to this divergence are studied, in particular the formula of integration by parts is derived. Specific examples include inner calculi on a non-commutative algebra, the Berezin integral on the supercircle and integrals on Hopf algebras.
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22

Ashraf, Mohammad, Aisha Jabeen та Nazia Parveen. "On Jordan triple (σ,τ)-higher derivation of triangular algebra". Special Matrices 6, № 1 (2018): 383–93. http://dx.doi.org/10.1515/spma-2018-0032.

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Abstract Let R be a commutative ring with unity, A = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module. In this article,we study Jordan triple (σ,τ)-higher derivation onAand prove that every Jordan triple (σ,τ)-higher derivation on A is a (σ,τ)-higher derivation on A.
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23

Krishna, Amalendu, and Husney Parvez Sarwar. "-THEORY OF MONOID ALGEBRAS AND A QUESTION OF GUBELADZE." Journal of the Institute of Mathematics of Jussieu 18, no. 5 (2017): 1051–85. http://dx.doi.org/10.1017/s1474748017000317.

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We show that for any commutative Noetherian regular ring $R$ containing $\mathbb{Q}$, the map $K_{1}(R)\rightarrow K_{1}\left(\frac{R[x_{1},\ldots ,x_{4}]}{(x_{1}x_{2}-x_{3}x_{4})}\right)$ is an isomorphism. This answers a question of Gubeladze. We also compute the higher $K$-theory of this monoid algebra. In particular, we show that the above isomorphism does not extend to all higher $K$-groups. We give applications to a question of Lindel on the Serre dimension of monoid algebras.
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24

Kleinfeld, Erwin, and Harry F. Smith. "Right alternative algebras with commutators in a nucleus." Bulletin of the Australian Mathematical Society 46, no. 1 (1992): 81–90. http://dx.doi.org/10.1017/s0004972700011692.

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Let A be a right alternative algebra, and [A, A] be the linear span of all commutators in A. If [A, A] is contained in the left nucleus of A, then left nilpotence implies nilpotence. If [A, A] is contained in the right nucleus, then over a commutative-associative ring with 1/2, right nilpotence implies nilpotence. If [A, A] is contained in the alternative nucleus, then the following structure results hold: (1) If A is prime with characteristic ≠ 2, then A is either alternative or strongly (–1, 1). (2) If A is a finite-dimensional nil algebra, over a field of characteristic ≠ 2, then A is nilpo
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25

Wu, Xiaoying, and Xiaohong Zhang. "The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal." Symmetry 10, no. 10 (2018): 465. http://dx.doi.org/10.3390/sym10100465.

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For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Seco
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26

Zhuchok, A. V. "The least dimonoid congruences on relatively free trioids." Matematychni Studii 57, no. 1 (2022): 23–31. http://dx.doi.org/10.30970/ms.57.1.23-31.

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When Loday and Ronco studied ternary planar trees, they introduced types of algebras,called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associativeoperations satisfying additional eight axioms relating these operations, while a trialgebra is justa linear analog of a trioid. If all operations of a trioid (trialgebra) coincide, we obtain the notionof a semigroup (associative algebra), and if two concrete operations of a trioid (trialgebra)coincide, we obtain the notion of a dimonoid (dialgebra) and so, trioids (trialgebras) are ageneralization of semigroups (as
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27

Bagio, Dirceu, Daiana Flôres, and Alveri Sant’ana. "Inner actions of weak Hopf algebras." Journal of Algebra and Its Applications 16, no. 06 (2017): 1750118. http://dx.doi.org/10.1142/s0219498817501183.

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Let [Formula: see text] be an associative ring and [Formula: see text] idempotent elements of [Formula: see text]. In this paper we introduce the notion of [Formula: see text]-invertibility for an element of [Formula: see text] and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra [Formula: see text] and an algebra [Formula: see text], we present sufficient conditions for [Formula: see text] to admit an inner action of [Formula: see text]. We also prove that if [Formula: see text] is a left [Formula: see text]-module algebra then [Formula: see text] acts innerly o
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28

Brown, Lawrence G. "Close hereditary C*-subalgebras and the structure of quasi-multipliers." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 2 (2017): 263–92. http://dx.doi.org/10.1017/s0308210516000172.

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We answer a question of Takesaki by showing that the following can be derived from the thesis of Shen: if A and B are σ-unital hereditary C*-subalgebras of C such that ‖p – q‖ < 1, where p and q are the corresponding open projections, then A and B are isomorphic. We give some further elaborations and counterexamples with regard to the σ-unitality hypothesis. We produce a natural one-to-one correspondence between complete order isomorphisms of C*-algebras and invertible left multipliers of imprimitivity bimodules. A corollary of the above two results is that any complete order isomorphism be
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Jakobsen, Hans Plesner. "Algebras of variable coefficient quantized differential operators." Journal of Mathematical Physics 63, no. 8 (2022): 081704. http://dx.doi.org/10.1063/5.0091631.

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In the framework of (vector valued) quantized holomorphic functions defined on non-commutative spaces, “quantized Hermitian symmetric spaces,” an obvious problem is to describe (quantum) holomorphically induced representations in terms of some manageable structures. An intimately related problem is to decide what the algebras of quantized differential operators with variable coefficients should be. It is an immediate point that even zeroth order operators, given as multiplications by polynomials, have to be specified as, e.g., left or right multiplication operators since the polynomial algebra
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KOVAČEVIĆ, DOMAGOJ, and STJEPAN MELJANAC. "KAPPA-MINKOWSKI SPACETIME, KAPPA-POINCARÉ HOPF ALGEBRA AND REALIZATIONS." International Journal of Geometric Methods in Modern Physics 09, no. 06 (2012): 1261009. http://dx.doi.org/10.1142/s0219887812610099.

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The κ-Minkowski spacetime and Lorentz algebra are unified in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincaré algebras are defined. They are determined by the matrix depending on momenta. Realizations and star product are defined and analyzed in general. The relation among the coproduct of momenta, realization and the star product is pointed out. Hopf algebra of the Poincaré algebra, related to the covariant realization, is presented in unified covariant form. Left–right dual realizations and dual algebra are introduced and
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31

KHARLAMPOVICH, OLGA, and ALEXEI MYASNIKOV. "UNDECIDABILITY OF THE FIRST ORDER THEORIES OF FREE NONCOMMUTATIVE LIE ALGEBRAS." Journal of Symbolic Logic 83, no. 3 (2018): 1204–16. http://dx.doi.org/10.1017/jsl.2017.80.

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AbstractLet R be a commutative integral unital domain and L a free noncommutative Lie algebra over R. In this article we show that the ring R and its action on L are 0-interpretable in L, viewed as a ring with the standard ring language $+ , \cdot ,0$. Furthermore, if R has characteristic zero then we prove that the elementary theory $Th\left( L \right)$ of L in the standard ring language is undecidable. To do so we show that the arithmetic ${\Bbb N} = \langle {\Bbb N}, + , \cdot ,0\rangle $ is 0-interpretable in L. This implies that the theory of $Th\left( L \right)$ has the independence prop
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32

Gumerov, R. N., and E. V. Lipacheva. "Topological Grading of Semigroup C*-Algebras." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 3 (90) (June 2020): 44–55. http://dx.doi.org/10.18698/1812-3368-2020-3-44-55.

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The paper deals with the abelian cancellative semigroups and the reduced semigroup C*-algebras. It is supposed that there exist epimorphisms from the semigroups onto the group of integers modulo n. For these semigroups we study the structure of the reduced semigroup C*-algebras which are also called the Toeplitz algebras. Such a C*-algebra can be defined for any non-abelian left cancellative semigroup. It is a very natural object in the category of C*-algebras because this algebra is generated by the left regular representation of a semigroup. In the paper, by a given epimorphism σ we construc
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33

Zhang, James J. "Quadratic algebras with few relations." Glasgow Mathematical Journal 39, no. 3 (1997): 323–32. http://dx.doi.org/10.1017/s0017089500032249.

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Throughout V will be a finite dimensional vector space over a field k and T(V) will denote the tensor algebra over V. For simplicity the symbol ⊗ will be omitted in the writing of the elements of T(V). Let be a basis of V ordered by Xi<Xi+1 for all i. Then we order the non-commutative monomials and 1 ≤ is ≤ n for s = 1,…, l} lexicographically from the left. D. Anick [1, p. 652] defines the high term of an element b in T(V) to be the highest monomial appearing in b. As a consequence of [1,3.2], if the set of the high terms of homogeneous relations is combinatorically free in the sense of no
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34

Lin, Hong-Yang, Marc Cahay, Badri N. Vellambi, and Dennis Morris. "A Generalization of Quaternions and Their Applications." Symmetry 14, no. 3 (2022): 599. http://dx.doi.org/10.3390/sym14030599.

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There are a total of 64 possible multiplication rules that can be defined starting with the generalized imaginary units first introduced by Hamilton. Of these sixty-four choices, only eight lead to non-commutative division algebras: two are associated to the left- and right-chirality quaternions, and the other six are generalizations of the split-quaternion concept first introduced by Cockle. We show that the 4×4 matrix representations of both the left- and right-chirality versions of the generalized split-quaternions are algebraically isomorphic and can be related to each other by 4×4 permuta
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35

YAPTI ÖZKURT, Zeynep. "Bases of fixed point subalgebras on nilpotent Leibniz algebras." Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 26, no. 1 (2024): 272–78. http://dx.doi.org/10.25092/baunfbed.1332488.

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Let K be a field of characteristic zero, X={x_(1,) x_2,…,x_n} and R_m={r_(1,) ,…,r_m} be two sets of variables, F be the free left nitpotent Leibniz algebra generated by X, and K[R_m ] be the commutative polynomial algebra generated by R_m over the base field K. The fixed point subalgebra of an automorphism φ is the subalgebra of F consisting of elements that are invariant under the automorphism. In this work, we consider specific automorphisms of F and determine the fixed point subalgebras of these automorphisms. Then, we find bases of these fixed point subalgebras. In addition, we get genera
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Avila, Julio Cesar, Martín Eduardo Frías-Armenta, and Elifalet López-González. "A-Differentiability over Associative Algebras." Mathematics 13, no. 10 (2025): 1619. https://doi.org/10.3390/math13101619.

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The unital associative algebra structure A on Rn allows for defining elementary functions and functions defined by convergent power series. For these, the usual derivative has a simple form even for higher-order derivatives, which allows us to have the A-calculus. Thus, we introduce A-differentiability. Rules for A-differentiation are obtained: a product rule, left and right quotients, and a chain rule. Convergent power series are A-differentiable, and their A-derivatives are the power series defined by their A-derivatives. Therefore, we use associative algebra structures to calculate the usua
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37

BAI, LI, and SHUANHONG WANG. "TWISTED DRINFELD DOUBLES AND REPRESENTATIONS OF A HOPF ALGEBRA." Journal of Algebra and Its Applications 11, no. 06 (2012): 1250118. http://dx.doi.org/10.1142/s0219498812501186.

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In this paper, we consider a class of non-commutative and non-cocommutative Hopf algebras Hp(α, q, m) and then show that these Hopf algebras can be realized as a quantum double of certain Hopf algebras with respect to Hopf skew pairings (Ap(q, m), Bp(q, m), τα). Furthermore, using the Hopf skew pairing with appropriate group homomorphisms: ϕ : π → Aut (Ap(q, m)) and ψ : π → Aut (Bp(q, m)), we construct a twisted Drinfeld double D(Ap(q, m), Bp(q, m), τ; ϕ, ψ) which is a Turaev [Formula: see text]-coalgebra, where the group [Formula: see text] is a twisted semi-direct square of a group π. Then w
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38

Stepanova, A. A. "S-acts over a Well-ordered Monoid with Modular Congruence Lattice." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 87–102. http://dx.doi.org/10.26516/1997-7670.2021.35.87.

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This work relates to the structural act theory. The structural theory includes the description of acts over certain classes of monoids or having certain properties, for example, satisfying some requirement for the congruence lattice. The congruences of universal algebra is the same as the kernels of homomorphisms from this algebra into other algebras. Knowledge of all congruences implies the knowledge of all the homomorphic images of the algebra. A left $S$–act over monoid $S$ is a set $A$ upon which $S$ acts unitarily on the left. In this paper, we consider $S$–acts over linearly ordered and
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39

Moldovyan, Dmitry, Alexander Moldovyan, and Denis Guryanov. "Blind signature protocols based on hidden discrete logarithm problem." Information and Control Systems, no. 3 (June 15, 2020): 71–78. http://dx.doi.org/10.31799/1684-8853-2020-3-71-78.

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Introduction: The progress in the development of quantum computing has raised the problem of constructing post-quantum two-key cryptographic algorithms and protocols, i.e. crypto schemes resistant to attacks from quantum computers. Based on the hidden discrete logarithm problem, some practical post-quantum digital signature schemes have been developed. The next step could be the development of post-quantum blind signature protocols. Purpose: To develop blind signature protocols based on the computational difficulty of the hidden discrete logarithm problem. Method: The use of blinding factors i
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40

Singh, Tejinder P. "Gravitation, and quantum theory, as emergent phenomena." Journal of Physics: Conference Series 2533, no. 1 (2023): 012013. http://dx.doi.org/10.1088/1742-6596/2533/1/012013.

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Abstract There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics – a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for
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41

Ashraf, Mohammad, Aisha Jabeen та Mohd Akhtar. "Generalized Jordan triple (σ,τ)-higher derivation on triangular algebras". Filomat 33, № 8 (2019): 2285–94. http://dx.doi.org/10.2298/fil1908285.

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Let R be a commutative ring with unity, U = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module. Let ? and ? be two automorphisms of U. A family ? = {?n}n?N of R-linear mappings ?n : U ? U is said to be a generalized Jordan triple (?,?)-higher derivation on A if there exists a Jordan triple (?,?)-higher derivation D = {dn}n?N on U such that ?0 = IU, the identity map of U and ?n(XYX) = ?i+j+k=n ?i(?n-i(X))dj(?k?i(Y))dk(?n-k(X)) holds for all X,Y ? U and each n ? N. In this article, we study g
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42

Gryshchuk, Serhii. "Monogenic functions in commutative complex algebras of the second rank and the Lamé equilibrium system for some class of plane orthotropy." Ukrainian Mathematical Bulletin 16, no. 3 (2019): 345–46. http://dx.doi.org/10.37069/1810-3200-2019-16-3-3.

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We consider a class of plane orthotropic deformations of the form \(\varepsilon_{x} = \sigma_x + a_{12} \sigma_y\), \(\gamma_{xy} = 2 \left(p-a_{12}\right) \tau_{xy}\), \(\varepsilon_{y}= a_{12}\sigma_x+\sigma_y\), where \(\sigma_x\), \(\tau_{xy}\), \(\sigma_y\) and \(\varepsilon_{x}\), \(\frac{\gamma_{xy}}{2}\), \(\varepsilon_{y}\) are components of the stress tensor and the deformation tensor, respectively, real parameters \(p\) and \(a_{12}\) satisfy the inequalities: \(-1 \lt p \lt 1\), \(-1 \lt a_{12} \lt p\). A class of solutions of the Lamé equilibrium system for displacements is built
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43

Alkenani, Ahmad N., Mohammad Ashraf та Aisha Jabeen. "Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras". Special Matrices 6, № 1 (2017): 216–28. http://dx.doi.org/10.1515/spma-2017-0008.

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Abstract Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module. Suppose that A = Tri(A,M,B) is a triangular algebra which is 2-torsion free and σ, Γ be automorphisms of A. A map δ:A→A (not necessarily linear) is called a multiplicative generalized (σ, Γ)-derivation (resp. multiplicative generalized Jordan (σ, Γ)-derivation) on A associated with a (σ, Γ)-derivation (resp. Jordan (σ, Γ)-derivation) d on A if δ(xy) = δ(x)r(y) + σ(x)d(y) (resp. σ(x<sup>2</s
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44

Bavula, V. V. "The Group of Automorphisms of the Algebra of one-Sided Inverses of a Polynomial Algebra. II." Proceedings of the Edinburgh Mathematical Society 58, no. 3 (2015): 543–80. http://dx.doi.org/10.1017/s0013091514000303.

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AbstractThe algebra of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting left (but not two-sided) inverses of the canonical generators of the algebra Pn. The algebra is isomorphic to the algebra of scalar integro-differential operators provided that char(K) = 0. Ignoring the non-Noetherian property, the algebra belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of automorphisms of the algebra and for the group of units of (both groups are huge). An analogu
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45

GOULD, VICTORIA, and MIKLÓS HARTMANN. "Coherency, free inverse monoids and related free algebras." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 1 (2016): 23–45. http://dx.doi.org/10.1017/s0305004116000505.

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AbstractA monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is the non-additive notion corresponding to that for a ring R stating that every finitely generated submodule of every finitely presented right R-module is finitely presented. For monoids (and rings) right coherency is an important finitary property which determines, amongst other things, the existence of a model companion of the class of right S-acts (right R-modules) and hence that the class of existentially closed right S-acts (right R-modules) is axiom
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46

Jespers, Eric, and Arne Van Antwerpen. "Left semi-braces and solutions of the Yang–Baxter equation." Forum Mathematicum 31, no. 1 (2019): 241–63. http://dx.doi.org/10.1515/forum-2018-0059.

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Abstract Let {r\colon X^{2}\rightarrow X^{2}} be a set-theoretic solution of the Yang–Baxter equation on a finite set X. It was proven by Gateva-Ivanova and Van den Bergh that if r is non-degenerate and involutive, then the algebra {K\langle x\in X\mid xy=uv\text{ if }r(x,y)=(u,v)\rangle} shares many properties with commutative polynomial algebras in finitely many variables; in particular, this algebra is Noetherian, satisfies a polynomial identity and has Gelfand–Kirillov dimension a positive integer. Lebed and Vendramin recently extended this result to arbitrary non-degenerate bijective solu
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47

Zhuchok, Anatolii. "Structure of relatively free n-tuple semigroups." Algebra and Discrete Mathematics 36, no. 1 (2023): 109–28. http://dx.doi.org/10.12958/adm2173.

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An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion was considered by Koreshkov in the context of the theory of n-tuple algebras of associative type. The n>1 pairwise interassociative semigroups give rise to an n-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of n-tuple semigroups. We present the constructions of the free n-tuple semigroup, the free commutative n-tuple semigroup, the free rectangular n-tuple semigroup, the free left (right) k-nilpotent n-tuple semigroup, the free k-
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48

Gryshchuk, Serhii. "Monogenic functions in two dimensional commutative algebras to equations of plane orthotropy." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 32 (December 28, 2018): 18–29. http://dx.doi.org/10.37069/1683-4720-2018-32-3.

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Among all two-dimensional commutative and assosiative algebras of the second rank with the unity \(e\) over the field of complex numbers \(\mathbb{C}\) we find a semi-simple algebra \(\mathbb{B}_{0} := \{c_1 e+c_2 \omega: c_k\in\mathbb{C}, k=1,2\}\), \(\omega^2=e\), containing a basis \((e_1,e_2)\), such that \( e_1^4 + 2p e_1^2 e_2^2 + e_2^4 = 0 \) for any fixed \( p \) such that \(-1 \lt p \gt 1 \). A domain \(\mathcal{B}_{1}=\{(e_1,e_2)\}\), \(e_1=e\), is discribed in an explicit form. We consider an approach of \(\mathbb{B}_{0}\)-valued ''analytic'' functions \(\Phi(xe_1+ye_2) = U_{1}(x,y)
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49

Kassem, M. S., and K. Rowlands. "The quasi-strict topology on the space of quasi-multipliers of a B*-algebra." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (1987): 555–66. http://dx.doi.org/10.1017/s0305004100066913.

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The notion of a left (right, double) multiplier may be regarded as a generalization of the concept of a multiplier to a non-commutative Banach algebra. Each of these is a special case of a more general object, namely that of a quasi-multiplier. The idea of a quasi-multiplier was first introduced by Akemann and Pedersen in ([1], §4), where they consider the quasi-multipliers of a C*-algebra. One of the defects of quasi-multipliers is that, at least a priori, there does not appear to be a way of multiplying them together. The general theory of quasi-multipliers of a Banach algebra A with an appr
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50

Dean, Samuel. "Duality and contravariant functors in the representation theory of artin algebras." Journal of Algebra and Its Applications 18, no. 06 (2019): 1950111. http://dx.doi.org/10.1142/s0219498819501111.

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We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring [Formula: see text] as the kernels of certain functors [Formula: see text] rather than of functors [Formula: see text] which are given by a pp-pair. This paper will give various algebraic characterizations of these functors in the case that [Formula: see text] is an artin algebra. Suppose that [Formula: see text] is an artin algebra. An additive functor [Formula: see text] preserves inverse limits and [Formula: see text] is finitely presented if and only if there is a sequence of na
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