Relevant bibliographies by topics / Left-commutative algebras

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Academic literature on the topic 'Left-commutative algebras'

Author: Grafiati
Published: 3 June 2025
Last updated: 6 July 2025

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Journal articles on the topic "Left-commutative algebras"

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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 left exchangeable), but examples are given to show that the converse is not true in general. An interior GE-algebra is constructed using a bordered interior GE-algebra with certain conditions, and an example is given to explain this.
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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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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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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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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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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-Bernstein theorem for pseudo-effect algebras.
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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 equivalent: (i) A is separable; and (ii) the C*-tensor product A [otimes ]minA is hereditarily projective. Howerever, there is a non-separable, hereditarily projective, commutative C*-algebra A contained in [Bscr ](H), where H is a separable Hilbert space.
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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 of all right mappings on positive implicative equality algebra makes a dual BCK-algebra.
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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 such algebras for some natural number m is also established.
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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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Book chapters on the topic "Left-commutative algebras"

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Yves, Diers. "Zariski Toposes." In Categories of Commutative Algebras. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535867.003.0008.

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Abstract The category of schemes on a Zariski category can be fully and left-exactly embedded in a large topos - its large Zariski topos -while the category of locally finitely presentable schemes can be fully and left-exactly embedded in a topos-its Zariski topos. Modelled toposes and locally modelled toposes can be defined relatively to a Zariski category. They efficiently play the role of ringed toposes and locally ringed toposes. The Zariski topos is the classifying topos for locally modelled toposes, and to any modelled topos is associated a universal locally modelled topos- its prime spectrum. In order to describe the relations existing between the different kinds of schemes, modelled spaces, modelled toposes, and Zariski toposes associated to different Zariski categories, it is time to introduce the notion of morphisms of Zariski categories. There are, in fact three notions: morphisms, geometrical morphisms, and cogeometrical morphisms.
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Lambek, Joachim. "From Categorial Grammar to Bilinear Logic." In Substructural Logics. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198537779.003.0008.

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Abstract The syntactic calculus, also known as ‘ bidirectional categorial grammar’, is a kind of logic without any structural rules, other than the obligatory reflexive law and cut-rule. It had been inspired by multilinear algebra and non-commutative ring theory and was developed with applications to linguistics in mind. Here we shall confine attention to the associative version, although a non-associative version has also been studied [L 1961, Kandulski 1988, Došen 1988, 1989]. It differs from a very rudimentary form of Girard’s linear logic [Girard 1987, 1989] by the absence of the interchange rule which licenses commutativity. Because of its roots in non-commutative algebra and syntax, all appearance of commutativity is forbidden. The notation, which goes back to a pre-historic collaboration with George Findlay, was carefully chosen to reflect this absence of commutativity: the order of two letters was never to be wantonly interchanged, yet all rules were to be preserved under left-right symmetry, the guiding slogan being ‘ symmetry without commutativity’. It must be admitted, however, that the notation, proposed for linguistics [L 1958] and ring theory [L 1966], caught on in neither field (with some recent exceptions in linguistics).
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Nebe Gabriele. "Self-dual codes and invariant theory." In NATO Science for Peace and Security Series - D: Information and Communication Security. IOS Press, 2009. https://doi.org/10.3233/978-1-60750-019-3-23.

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A formal notion of a Typ T of a self-dual linear code over a finite left R-module V is introduced which allows to give explicit generators of a finite complex matrix group, the associated Clifford-Weil group C(T) ≤ GL|V|(C), such that the complete weight enumerators of self-dual isotropic codes of Type T span the ring of invariants of 𝒞(T). This generalizes Gleason’s 1970 theorem to a very wide class of rings and also includes multiple weight enumerators (see Section 2.7), as these are the complete weight enumerators cwem(C) = cwe(Rm⊗ C) of Rm × m-linear self-dual codes Rm⊗ C ≤ (Vm)Nof Type Tmwith associated Clifford-Weil group 𝒞m(T) = 𝒞(Tm). The finite Siegel &PHgr;-operator mapping cwem(C) to cwem−1(C) hence defines a ring epimorphism &PHgr;m: Inv(𝒞m(T)) ⇒ Inv(𝒞m−1(T)) between invariant rings of complex matrix groups of different degrees. If R = V is a finite field, then the structure of 𝒞m(T) allows to define a commutative algebra of 𝒞m(T) double cosets, called a Hecke algebra in analogy to the one in the theory of lattices and modular forms. This algebra consists of self-adjoint linear operators on Inv(𝒞m(T)) commuting with &PHgr;m. The Hecke-eigenspaces yield explicit linear relations among the cwemof self-dual codes C ≤ VN.
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