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Journal articles on the topic 'Finite associative algebra'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Alahmadi, Adel, and Fawziah Alharthi. "Finite Generation of Lie Derived Powers of Skew Lie Algebras." Algebra Colloquium 29, no. 02 (2022): 217–20. http://dx.doi.org/10.1142/s1005386722000177.

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Let [Formula: see text] be a finitely generated associative algebra over a field of characteristic different from 2. Herstein asked when the Lie algebra [Formula: see text] is finitely generated. Recently, it was shown that for a finitely generated nil algebra [Formula: see text] all derived powers of [Formula: see text] are finitely generated Lie algebras. Let [Formula: see text] be the Lie algebra of skew-symmetric elements of an associative algebra with involution. We consider all derived powers of the Lie algebra [Formula: see text] and prove that for any finitely generated associative nil

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2

Gordienko, A. S. "Co-stability of Radicals and Its Applications to PI-Theory." Algebra Colloquium 23, no. 03 (2016): 481–92. http://dx.doi.org/10.1142/s1005386716000468.

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We prove that if A is a finite-dimensional associative H-comodule algebra over a field F for some involutory Hopf algebra H not necessarily finite-dimensional, where either char F = 0 or char F > dim A, then the Jacobson radical J(A) is an H-subcomodule of A. In particular, if A is a finite-dimensional associative algebra over such a field F, graded by any group, then the Jacobson radical J(A) is a graded ideal of A. Analogous results hold for nilpotent and solvable radicals of finite-dimensional Lie algebras over a field of characteristic 0. We use the results obtained to prove the analog

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3

Iovanov, Miodrag Cristian, and Alexander Harris Sistko. "Maximal subalgebras of finite-dimensional algebras." Forum Mathematicum 31, no. 5 (2019): 1283–304. http://dx.doi.org/10.1515/forum-2019-0033.

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AbstractWe study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field {\mathbb{K}} and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case and then lifting to non-semisimple algebras. The results are sharpest in the case of algebraically closed fields and take special forms for algebras presented by quivers with relations. We also relate representation theoretic properties of the algebra and its maximal and other subalgebras and provide a series of embe

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4

Alhussein, H., and P. Kolesnikov. "Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules." Journal of Mathematical Physics 64, no. 4 (2023): 041701. http://dx.doi.org/10.1063/5.0146223.

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In this work, we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal algebra relative to the locality N = 2. In order to obtain this result, we adjust the algebraic discrete Morse theory to the case of differential algebras.

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5

Gordienko, A. S. "On H-simple not necessarily associative algebras." Journal of Algebra and Its Applications 18, no. 09 (2019): 1950162. http://dx.doi.org/10.1142/s0219498819501627.

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An algebra [Formula: see text] with a generalized [Formula: see text]-action is a generalization of an [Formula: see text]-module algebra where [Formula: see text] is just an associative algebra with [Formula: see text] and a relaxed compatibility condition between the multiplication in [Formula: see text] and the [Formula: see text]-action on [Formula: see text] holds. At first glance, this notion may appear too general, however, it enables to work with algebras endowed with various kinds of additional structures (e.g. comodule algebras over Hopf algebras, graded algebras, algebras with an ac

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6

Jaíyéọlá, Tèmítọ́pẹ́, Emmanuel Ilojide, Memudu Olatinwo, and Florentin Smarandache. "On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)." Symmetry 10, no. 10 (2018): 427. http://dx.doi.org/10.3390/sym10100427.

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In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be as

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7

Shestakov, Ivan, and Efim Zelmanov. "A finite presentation of Jordan algebras." International Journal of Algebra and Computation 28, no. 08 (2018): 1705–16. http://dx.doi.org/10.1142/s0218196718400155.

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Let [Formula: see text] be an associative algebra. Let [Formula: see text] be an involution. We study the following question: when are the Jordan algebras [Formula: see text] and [Formula: see text] finitely presented?

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8

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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9

Bahturin, Y. A., and A. Giambruno. "Group Gradings on Associative Algebras with Involution." Canadian Mathematical Bulletin 51, no. 2 (2008): 182–94. http://dx.doi.org/10.4153/cmb-2008-020-7.

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AbstractIn this paper we describe the group gradings by a finite abelian group G of the matrix algebra Mn(F) over an algebraically closed field F of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all G-gradings on all finite-dimensional involution simple algebras.

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10

Zhang, Xuemei, and Jianhua Zhou. "Centroids of Differentiably Simple Color Algebras." Algebra Colloquium 13, no. 03 (2006): 447–54. http://dx.doi.org/10.1142/s1005386706000393.

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The chains of ideals of differentiably simple (non-associative) color algebras and those of their centroids are studied. It is proved that for any finite-dimensional differentiably simple (non-associative) color algebra A and any set D of its color derivations, A is D-simple if and only if its centroid 𝙲(A) is D*-simple, where 𝙲(A) is a unitary ∊-commutative associative color algebra, and D* is the set of the color derivations determined by D.

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11

Shpakivskyi, Vitalii. "Conformable fractional derivative in commutative algebras." Ukrainian Mathematical Bulletin 20, no. 2 (2023): 269–82. http://dx.doi.org/10.37069/1810-3200-2023-20-2-7.

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In this paper, an analog of the conformable fractional derivative is defined in an arbitrary finite-dimensional commutative associative algebra. Functions taking values in the indicated algebras and having derivatives in the sense of a conformable fractional derivative are called $\varphi$% -monogenic. A relation between the concepts of $\varphi$-monogenic and monogenic functions in such algebras has been established. Two new definitions have been proposed for the fractional derivative of the functions with values in finite-dimensional commutative associative algebras.

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12

Alahmadi, Adel, and Hamed Alsulami. "Finite generation of Lie derived powers of associative algebras." Journal of Algebra and Its Applications 18, no. 03 (2019): 1950059. http://dx.doi.org/10.1142/s0219498819500592.

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Let [Formula: see text] be an associative algebra over a field of characteristic [Formula: see text] that is generated by a finite collection of nilpotent elements. We prove that all Lie derived powers of [Formula: see text] are finitely generated Lie algebras.

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13

da Silva Macedo, David Levi, and Plamen Koshlukov. "Codimension growth for weak polynomial identities, and non-integrality of the PI exponent." Proceedings of the Edinburgh Mathematical Society 63, no. 4 (2020): 929–49. http://dx.doi.org/10.1017/s0013091520000243.

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Let K be a field of characteristic zero. In this paper, we study the polynomial identities of representations of Lie algebras, also called weak identities, or identities of pairs. These identities are determined by pairs of the form (A, L) where A is an associative enveloping algebra for the Lie algebra L. Then a weak identity of (A, L) (or an identity for the representation of L associated to A) is an associative polynomial which vanishes when evaluated on elements of L⊆ A. One of the most influential results in the area of PI algebras was the theory developed by Kemer. A crucial role in it w

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14

Allison, Bruce, and Oleg Smirnov. "Coordinatization Theorems For Graded Algebras." Canadian Mathematical Bulletin 45, no. 4 (2002): 451–65. http://dx.doi.org/10.4153/cmb-2002-048-4.

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AbstractIn this paper we study simple associative algebras with finite -gradings. This is done using a simple algebra Fg that has been constructed in Morita theory from a bilinear form g : U × V → A over a simple algebra A. We show that finite -gradings on Fg are in one to one correspondence with certain decompositions of the pair (U, V). We also show that any simple algebra R with finite -grading is graded isomorphic to Fg for some bilinear from g : U × V → A, where the grading on Fg is determined by a decomposition of (U, V) and the coordinate algebra A is chosen as a simple ideal of the zer

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15

KOLESNIKOV, PAVEL. "ON THE WEDDERBURN PRINCIPAL THEOREM IN CONFORMAL ALGEBRAS." Journal of Algebra and Its Applications 06, no. 01 (2007): 119–34. http://dx.doi.org/10.1142/s0219498807002120.

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We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal semisimple factor of this algebra is unital, but does not hold in general.

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16

Drensky, Vesselin. "Weak polynomial identities and their applications." Communications in Mathematics 29, no. 2 (2021): 291–324. http://dx.doi.org/10.2478/cm-2021-0022.

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Abstract Let R be an associative algebra over a field K generated by a vector subspace V. The polynomial f(x 1, . . . , xn ) of the free associative algebra K〈x 1, x 2, . . .〉 is a weak polynomial identity for the pair (R, V) if it vanishes in R when evaluated on V. We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three.

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17

Maisuradze, M. V., and А. А. Mikhalev. "Primitive elements of free non-associative algebras over finite fields." Программирование, no. 2 (April 15, 2024): 84–92. http://dx.doi.org/10.31857/s0132347424020115.

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The representation of elements of free non-associative algebras as a set of multidimensional tables of coefficients is defined. An operation for finding partial derivatives for elements of free non-associative algebras in the same form is considered. Using this representation, a criterion of primitivity for elements of lengths 2 and 3 in terms of matrix ranks, as well as a primitivity test for elements of arbitrary length, is derived. This test makes it possible to estimate the number of primitive elements in free non-associative algebras with two generators over a finite field. The proposed r

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18

Kępczyk, Marek. "A Note on Algebras that are Sums of Two Subalgebras." Canadian Mathematical Bulletin 59, no. 2 (2016): 340–45. http://dx.doi.org/10.4153/cmb-2015-082-6.

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AbstractWe study an associative algebra A over an arbitrary field that is a sum of two subalgebras B and C (i.e., A = B+C). We show that if B is a right or left Artinian PI algebra and C is a PI algebra, then A is a PI algebra. Additionally, we generalize this result for semiprime algebras A. Consider the class of all semisimple finite dimensional algebras A = B + C for some subalgebras B and C that satisfy given polynomial identities f = 0 and g = 0, respectively. We prove that all algebras in this class satisfy a common polynomial identity.

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19

Kadison, Richard V., and Zhe Liu. "Derivations of Murray-von Neumann Algebras." MATHEMATICA SCANDINAVICA 115, no. 2 (2014): 206. http://dx.doi.org/10.7146/math.scand.a-19223.

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A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we study derivations of Murray-von Neumann algebras and their properties. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a von Neumann algebra of type ${\rm II}_1$ into that von Neumann algebra is 0. This result is an extension, in two ways, of Singer's seminal result

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20

Rocha, Josimar da Silva. "Associative Algebras Satisfying Quadratic Equations." Asian Research Journal of Mathematics 21, no. 6 (2025): 109–25. https://doi.org/10.9734/arjom/2025/v21i6947.

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This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X2 = aX + b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. The results obtained were validated computationally using the GAP system.

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21

Sweet, L. G., and J. A. MacDougall. "Algebras with Transitive Automorphism Groups." Canadian Mathematical Bulletin 29, no. 2 (1986): 224–26. http://dx.doi.org/10.4153/cmb-1986-036-1.

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AbstractLet A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.

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22

Alarfeen, Ahmad, Izzat Qaralleh, and Azhana Ahmad. "Properties of Nilpotent Evolution Algebras with no Maximal Nilindex." European Journal of Pure and Applied Mathematics 14, no. 1 (2021): 278–300. http://dx.doi.org/10.29020/nybg.ejpam.v14i1.3912.

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As a system of abstract algebra, evolution algebras are commutative and non-associative algebras. There is no deep structure theorem for general non-associative algebras. However, there are deep structure theorem and classification theorem for evolution algebras because it has been introduced concepts of dynamical systems to evolution algebras. Recently, in [25], it has been studied some properties of nilpotent evolution algebra with maximal index (dim E2 = dim E âˆ’ 1). This paper is devoted to studying nilpotent finite-dimensional evolution algebras E with dim E2 =dim E âˆ’ 2. We describe Li

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23

Minaiev, Pavlo, and Oleksandr Pypka. "On Schur-type theorem for Leibniz 3-algebras." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2024): 22–25. http://dx.doi.org/10.17721/1812-5409.2024/1.3.

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One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group G/ζ(G) of a group G is finite, then its derived subgroup [G,G] is also finite. This theorem was proved by B. Neumann in 1951. This result has numerous generalizations and modifications in group theory. At the same time, similar investigations were conducted in other algebraic structures, namely in modules, linear groups, topological groups, n-groups, associative algebras, Lie algebras, Lie n-algebras. In 2016, L.A. Kurdachenko, J. Otal and O.O. Pypka proved an analogue of Schur

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24

Rakhimov, I. S. "Algebraic Structures on Two-Dimensional Vector Space Over Any Basic Field." Malaysian Journal of Mathematical Sciences 18, no. 2 (2024): 227–57. http://dx.doi.org/10.47836/mjms.18.2.02.

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In the paper we utilize a new approach to the classification problem of finite-dimensional algebras. We give a complete classifications of associative and diassociative algebra structures on two-dimensional vector space over any basic field.

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25

BIRMAJER, DANIEL. "CONSTRUCTING FULL BLOCK TRIANGULAR REPRESENTATIONS OF ALGEBRAS." Journal of Algebra and Its Applications 06, no. 02 (2007): 259–65. http://dx.doi.org/10.1142/s021949880700217x.

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Every finite dimensional representation of an algebra is equivalent to a finite direct sum of indecomposable representations. Hence, the classification of indecomposable representations of algebras is a relevant (and usually complicated) task. In this note we study the existence of full block triangular representations, an interesting example of indecomposable representations, from a computational perspective. We describe an algorithm for determining whether or not an associative finitely presented k-algebra R has a full block triangular representation over [Formula: see text].

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26

Torrecillas, José Gómez. "Gelfand-Kirillov dimension of multi-filtered algebras." Proceedings of the Edinburgh Mathematical Society 42, no. 1 (1999): 155–68. http://dx.doi.org/10.1017/s0013091500020083.

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We consider associative algebras filtered by the additive monoid ℕp. We prove that, under quite general conditions, the study of Gelfand-Kirillov dimension of modules over a multi-filtered algebra R can be reduced to the associated ℕp-graded algebra G(R). As a consequence, we show the exactness of the Gelfand-Kirillov dimension when the multi-filtration is finite-dimensional and G(R) is a finitely generated noetherian algebra. Our methods apply to examples like iterated Ore extensions with arbitrary derivations and “homothetic” automorphisms (e.g. quantum matrices, quantum Weyl algebras) and t

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27

Lee, Jongwoo, Seul Hee Choi, and Ki-Bong Nam. "Non-associative Algebras with n-Exponential Functions." Algebra Colloquium 16, no. 01 (2009): 85–94. http://dx.doi.org/10.1142/s1005386709000108.

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Der non (𝔽[x1, x2, …, xn]Mn) of the evaluation algebra 𝔽[x1, x2, …, xn]Mn and Der non (𝔽[e± x1, e± x2, …, e± xn]Mn) of the evaluation algebra 𝔽[e± x1, e± x2, …, e± xn]Mn are found in [2] and [4], respectively, where Mn = {∂1, …, ∂n}. In this work we find [Formula: see text] of the algebra [Formula: see text]. We define a finite dimensional semi-Lie algebra which is simple. We define a simple semi-Lie ring whose dimension is finite.

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28

N.H, Minh, and Moldovyan D.N, et al. "POST-QUANTUM BLIND SIGNATURE PROTOCOL ON NON-COMMUTATIVE ALGEBRAS." Journal of Computer Science and Cybernetics 37, no. 4 (2021): 495–509. http://dx.doi.org/10.15625/1813-9663/37/4/16023.

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A method for constructing a blind signature scheme based on a hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. Blind signature protocols are constructed using four-dimensional and six-dimensional algebras defined over a ground finite field GF(p) and containing a global two-sided unit as an algebraic support. The basic properties of the used algebra, which determine the choice of protocol parameters, are described.

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N.H, Minh, and Moldovyan D.N, et al. "POST-QUANTUM BLIND SIGNATURE PROTOCOL ON NON-COMMUTATIVE ALGEBRAS." Journal of Computer Science and Cybernetics 37, no. 4 (2021): 495–509. http://dx.doi.org/10.15625/1813-9663/37/4/16023.

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A method for constructing a blind signature scheme based on a hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. Blind signature protocols are constructed using four-dimensional and six-dimensional algebras defined over a ground finite field GF(p) and containing a global two-sided unit as an algebraic support. The basic properties of the used algebra, which determine the choice of protocol parameters, are described.

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30

Das, Apurba. "Cohomology and deformations of weighted Rota–Baxter operators." Journal of Mathematical Physics 63, no. 9 (2022): 091703. http://dx.doi.org/10.1063/5.0093066.

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Weighted Rota–Baxter operators on associative algebras are closely related to modified Yang–Baxter equations, splitting of algebras, and weighted infinitesimal bialgebras and play an important role in mathematical physics. For any λ ∈ k, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by λ-weighted relative Rota–Baxter operators. Using such characterization, we define the cohomology of a λ-weighted relative Rota-Baxter operator T and interpret this as the Hochschild cohomology of a suitable algebra with coefficients in an appropriate bimodule. We study lin

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31

Assem, Ibrahim, and Peter Brown. "Strongly simply connected Auslander algebras." Glasgow Mathematical Journal 39, no. 1 (1997): 21–27. http://dx.doi.org/10.1017/s0017089500031864.

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Letkbe an algebraically closed field. By an algebra is meant an associative finite dimensionalk-algebra A with an identity. We are interested in studying the representation theory of Λ, that is, in describing the category mod Λ of finitely generated right Λ-modules. Thus we may, without loss of generality, assume that Λ is basic and connected. For our purpose, one strategy consists in using covering techniques to reduce the problem to the case where the algebra is simply connected, then in solving the problem in this latter case. This strategy was proved efficient for representation-finite alg

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32

Moldovyan, Dmitriy, Alexandr Moldovyan, and Nikolay Moldovyan. "Structure of a finite non-commutative algebra set by a sparse multiplication table." Quasigroups and Related Systems 30, no. 1(47) (2022): 133–40. http://dx.doi.org/10.56415/qrs.v30.11.

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Four-dimensional finite non-commutative associative algebras represent practical interest as algebraic support of post-quantum digital signature algorithms, especially algebras with two sided global unit, set by sparse basis vectors multiplication tables. A new algebra of the latter type, set over the field GF(p), is proposed and its structure is investigated. The studied algebra is described as a set of p2 + p + 1 commutative subalgebras of three different types. All subalgebras intersect strictly in the subset of scalar vectors. Formulas are derived for the number of subalgebras of each type

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BOUDI, N., H. MARHNINE, C. ZARHOUTI, A. FERNANDEZ LOPEZ, and E. GARCIA RUS. "Noetherian Banach Jordan pairs." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 25–36. http://dx.doi.org/10.1017/s0305004100004709.

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An associative or alternative algebra A is Noetherian if it satisfies the ascending chain condition on left ideals. Sinclair and Tullo [21] showed that a complex Noetherian Banach associative algebra is finite dimensional. This result was extended by Benslimane and Boudi [5] to the alternative case.For a Jordan algebra J or a Jordan pair V, the suitable Noetherian condition is the ascending chain condition on inner ideals. In a recent work Benslimane and Boudi [6] proved that a complex Noetherian Banach Jordan algebra is finite dimensional.Here we show the following results:(i) the Jacobson ra

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34

Lee, Jongwoo, and Ki-Bong Nam. "New Simple Algebras Containing the Matrix Ring." Algebra Colloquium 18, spec01 (2011): 775–84. http://dx.doi.org/10.1142/s1005386711000654.

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We define the combinatorial simple algebras N(eAS,n,t)k, N(eAS,n,t)k+and N(eAS,n,t)[k]which contain both the matrix ring and the non-associative algebras discussed in [11]. We also define a new cyclic finite dimensional algebra which contains the matrix ring Mn(𝔽) and show that the algebra is simple (see [3] and [7]). Even more, we find the automorphism group of the algebra N(0,n,t)[1]and show that the general matrix group GLn+t(𝔽) is not a subgroup of the automorphism group Aut (N(0,n,t)[1]).

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35

Losev, Ivan, and Victor Ostrik. "Classification of finite-dimensional irreducible modules over -algebras." Compositio Mathematica 150, no. 6 (2014): 1024–76. http://dx.doi.org/10.1112/s0010437x13007604.

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AbstractFinite $W$-algebras are certain associative algebras arising in Lie theory. Each $W$-algebra is constructed from a pair of a semisimple Lie algebra ${\mathfrak{g}}$ (our base field is algebraically closed and of characteristic 0) and its nilpotent element $e$. In this paper we classify finite-dimensional irreducible modules with integral central character over $W$-algebras. In more detail, in a previous paper the first author proved that the component group $A(e)$ of the centralizer of the nilpotent element under consideration acts on the set of finite-dimensional irreducible modules o

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Arzikulov, Farhodjon, Furqatjon Urinboyev, and Shahlo Ergasheva. "A CHARACTERIZATION OF DERIVATIONS AND AUTOMORPHISMS ON SOME SIMPLE ALGEBRAS." Ural Mathematical Journal 8, no. 2 (2022): 46. http://dx.doi.org/10.15826/umj.2022.2.004.

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In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra \(\mathcal{D}\) and the seven-dimensional central simple commutative algebra \(\mathcal{C}\). We prove that every local derivation of these algebras \(\

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F.N., Arzikulov, and Nuriddinov O.O. "Description of Local Derivations on Jordan Algebras of Dimension Five." Владикавказский математический журнал 26, no. 4 (2024): 28–43. http://dx.doi.org/10.46698/y5752-5645-6737-n.

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In the present paper we investigate local derivations on finite dimensional Jordan algebras. The Gleason--Kahane--\.{Z}elazko theorem, which is a fundamental contribution in the theory of Banach algebras, asserts that every unital linear functional $F$ on a complex unital Banach algebra $A$, such that $F(a)$ belongs to the spectrum $\sigma(a)$ of $a$ for every $a\in A,$ is multiplicative. In modern terminology this is equivalent to the following condition: every unital linear local homomorphism from a unital complex Banach algebra $A$ into ${\Bbb C}$ is multiplicative. We recall that a linear

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Lopes, Jonas Gonçalves. "On strongly associative group algebras of p-solvable groups." Journal of Algebra and Its Applications 14, no. 06 (2015): 1550085. http://dx.doi.org/10.1142/s0219498815500851.

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Given a partial action α of a group G on the group algebra FH, where H is a finite group and F is a field whose characteristic p divides the order of H, we investigate the associativity question of the partial crossed product FH *α G. If FH *α G is associative for any G and any α, then FH is called strongly associative. We characterize the strongly associative modular group algebras FH with H being a p-solvable group.

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39

Wu, Henan. "Finite irreducible representations of map Lie conformal algebras." International Journal of Mathematics 28, no. 01 (2017): 1750002. http://dx.doi.org/10.1142/s0129167x17500021.

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In this paper, we study the finite representation theory of the map Lie conformal algebra [Formula: see text], where G is a finite simple Lie conformal algebra and A is a commutative associative algebra with unity over [Formula: see text]. In particular, we give a complete classification of nontrivial finite irreducible conformal modules of [Formula: see text] provided A is finite-dimensional.

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Shpakivskyi, Vitalii. "σ-monogenic functions in commutative algebras". Proceedings of the International Geometry Center 16, № 1 (2023): 17–41. http://dx.doi.org/10.15673/tmgc.v16i1.2421.

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In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.

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BERNIK, J., R. DRNOVŠEK, D. KOKOL BUKOVŠEK, T. KOŠIR, M. OMLADIČ, and H. RADJAVI. "ON SEMITRANSITIVE JORDAN ALGEBRAS OF MATRICES." Journal of Algebra and Its Applications 10, no. 02 (2011): 319–33. http://dx.doi.org/10.1142/s0219498811004616.

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A set [Formula: see text] of linear operators on a vector space is said to be semitransitive if, given nonzero vectors x, y, there exists [Formula: see text] such that either Ax = y or Ay = x. In this paper we consider semitransitive Jordan algebras of operators on a finite-dimensional vector space over an algebraically closed field of characteristic not two. Two of our main results are: (1) Every irreducible semitransitive Jordan algebra is actually transitive. (2) Every semitransitive Jordan algebra contains, up to simultaneous similarity, the upper triangular Toeplitz algebra, i.e. the unit

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Mayr, Peter, and Nik Ruškuc. "Presentations for Subrings and Subalgebras of Finite CO-Rank." Quarterly Journal of Mathematics 71, no. 1 (2019): 53–71. http://dx.doi.org/10.1093/qmathj/haz033.

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Abstract Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented (resp. finitely generated) if and only if $B$ is finitely presented (resp. finitely generated). As corollaries, we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the

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43

Moldovyan, Alexandr A., and Dmitriy N. Moldovyan. "A New Method for Developing Signature Algorithms on Finite Non-commutative Algebras." Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1(98) (July 2022): 56–65. http://dx.doi.org/10.56415/basm.y2022.i1.p56.

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A new method for developing signature schemes on finite non-commutative associative algebras is introduced. A signature algorithm is developed on a 4-dimensional algebra defined over the ground field $GF(p)$. The public key element and one of the signature elements represent vectors calculated using exponentiation operations in a hidden commutative group. Decomposition of the algebra into commutative subalgebras is taken into account while designing the algorithm. The method extends the class of algebraic digital signature schemes and opens up the possibility of developing a number of practica

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LOPATIN, ARTEM A., and IVAN P. SHESTAKOV. "ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS." International Journal of Algebra and Computation 23, no. 08 (2013): 1881–94. http://dx.doi.org/10.1142/s0218196713500471.

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We study the nilpotency degree of a relatively free finitely generated associative algebra with the identity xn = 0 over a finite field 𝔽 with q elements. In the case of q ≥ n the nilpotency degree is proven to be the same as in the case of an infinite field of the same characteristic. In the case of q = n - 1 it is shown that the nilpotency degree differs from the nilpotency degree for an infinite field of the same characteristic by at most one. The nilpotency degree is explicitly computed for n = 3.

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Minaiev, P. Ye, O. O. Pypka, and I. V. Shyshenko. "On Poisson (2-3)-algebras which are finite-dimensional over the center." Researches in Mathematics 32, no. 1 (2024): 118. http://dx.doi.org/10.15421/242411.

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One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous generalizations and modifications in group theory. At the same time, similar investigations were conducted in other algebraic structures, namely in modules, linear groups, topological groups, $n$-groups, associative algebras, Lie algebras, Lie $n$-algebras, Lie rings, Leibniz algebras. In 2021, L.A. Kurdachenko, O.O. Pypka and I.Ya. Subbotin proved an analogue of Sc

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VERSTEGEN, DIRK. "ON THE CLASSIFICATION OF W-ALGEBRAS." International Journal of Modern Physics A 10, no. 10 (1995): 1413–48. http://dx.doi.org/10.1142/s0217751x95000681.

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We review and extend the conformal bootstrap approach to the classification of quantum W-algebras. These are extensions of the Virasoro algebra by a finite set of primary fields. Explicit forms are given for the most general crossing-symmetric four-point functions. Together with a large c expansion of the conformal blocks, this gives a powerful tool for finding all W-algebras that are associative for generic values of the central charge c.

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KEMER, ALEXANDER. "MULTILINEAR IDENTITIES OF THE ALGEBRAS OVER A FIELD OF CHARACTERISTIC P." International Journal of Algebra and Computation 05, no. 02 (1995): 189–97. http://dx.doi.org/10.1142/s0218196795000124.

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CENTRONE, LUCIO. "A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS." Journal of Algebra and Its Applications 10, no. 05 (2011): 865–89. http://dx.doi.org/10.1142/s0219498811004987.

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In this paper, we consider associative P.I. algebras over a field F of characteristic 0, graded by a finite group G. More precisely, we define the G-graded Gelfand–Kirillov dimension of a G-graded P.I. algebra. We find a basis of the relatively free graded algebras of the upper triangular matrices UTn(F) and UTn(E), with entries in F and in the infinite-dimensional Grassmann algebra, respectively. As a consequence, we compute their graded Gelfand–Kirillov dimension with respect to the natural gradings defined over these algebras. We obtain similar results for the upper triangular matrix algebr

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Pogorzały, Zygmunt. "Algebras stably equivalent to selfinjective algebras whose Auslander-Reiten quivers consist only of generalized standard components." Glasgow Mathematical Journal 40, no. 1 (1998): 1–19. http://dx.doi.org/10.1017/s0017089500032316.

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Throughout the paper K denotes a fixed algebraically closed field. All algebras considered are finite-dimensional associative K-algebras with a unit element. Moreover, they are assumed to be basic and connected. For an algebra A we denote by mod(A) the category of all finitely generated right A-modules, and mod(A) denotes the stable category of mod(A), i.e. mod(A)/℘ where ℘ is the two-sided ideal in mod(A) of all morphisms that factorize through projective A-modules. Two algebras A and B are said to be stably equivalent if the stable categories mod(A) and mod(B) are equivalent. The study of st

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MAGNANO, G., and F. MAGRI. "POISSON-NIJENHUIS STRUCTURES AND SATO HIERARCHY." Reviews in Mathematical Physics 03, no. 04 (1991): 403–66. http://dx.doi.org/10.1142/s0129055x91000151.

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We show that the direct sum of n copies of a Lie algebra is endowed with a sequence of affine Lie-Poisson brackets, which are pairwise compatible and define a multi-Hamiltonian structure; to this structure one can associate a recursion operator and a Kac-Moody algebra of Hamiltonian vector fields. If the initial Lie algebra is taken to be an associative algebra of differential operators, a suitable family of Hamiltonian vector fields reproduce either the n-th Gel'fand-Dikii hierarchy (for n finite) or Sato's hierarchy (for n = ∞). Within the same framework, it is also possible to recover a cla

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