Relevant bibliographies by topics / Finite associative algebra

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Finite associative algebra'

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Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Finite associative algebra"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Finite associative algebra"

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Bogdanic, Dusko. "Graded blocks of group algebras." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:faeaaeab-1fe6-46a9-8cbb-f3f633131a73.

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In this thesis we study gradings on blocks of group algebras. The motivation to study gradings on blocks of group algebras and their transfer via derived and stable equivalences originates from some of the most important open conjectures in representation theory, such as Broue’s abelian defect group conjecture. This conjecture predicts the existence of derived equivalences between categories of modules. Some attempts to prove Broue’s conjecture by lifting stable equivalences to derived equivalences highlight the importance of understanding the connection between transferring gradings via stabl
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Shlaka, Hasan Mohammed Ali Saeed. "Jordan-Lie inner ideals of finite dimensional associative algebras." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42787.

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A subspace B of a Lie algebra L is said to be an inner ideal if [B, [B,L]] ⊆ B. Suppose that L is a Lie subalgebra of an associative algebra A. Then an inner ideal B of L is said to be Jordan-Lie if B2 = 0. In this thesis, we study Jordan-Lie inner ideals of finite dimensional associative algebras (with involution) and their corresponding Lie algebras over an algebraically closed field F of characteristic not 2 or 3. Let A be a finite dimensional associative algebra over F. Recall that A becomes a Lie algebra A(-) under the Lie bracket defined by [x,y] = xy - yx for all x,y ∈ A. Put A(0) = A(-
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Bastian, Nicholas Lee. "Terwilliger Algebras for Several Finite Groups." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8897.

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In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the ca
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Wesche, Morten Verfasser], and Bettina [Akademischer Betreuer] [Eick. "Enumeration of class 2 associative algebras over finite fields / Morten Wesche ; Betreuer: Bettina Eick." Braunschweig : Technische Universität Braunschweig, 2018. http://d-nb.info/1175814725/34.

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Gawell, Elin. "Centra of Quiver Algebras." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-106734.

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A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. We describe the center of a partly (anti-)commutative quiveralgebra and state necessary and sufficient conditions for the center to be finitely genteratedas a K-algebra.Examples are provided of partly (anti-)commutative quiver algebras that are Koszul
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Sadaka, Guilnard. "Paires admissibles d'une algèbre de Lie simple complexe et W-algèbres finies." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2309/document.

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Soient g une algèbre de Lie simple complexe et e un élément nilpotent de g. Nous nous intéressons dans ce mémoire à la question (soulevée par Premet) d'isomorphisme entre les W-algèbres finies construites à partir de certaines sous-algèbres nilpotentes de g dites e-admissibles. Nous introduisons les notions de paire et graduation e-admissibles. Nous montrons ensuite que la W-algèbre associée à une paire e-admissible possède des propriétés similaires à celle introduite par Gan et Ginzburg. De plus, nous définissons une relation d'équivalence sur l'ensemble des paires admissibles. Nous montrons
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Jastrzębska, Małgorzata. "Kraty anihilatorów w pewnych klasach algebr." Doctoral thesis, 2015. https://depotuw.ceon.pl/handle/item/1474.

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W literaturze pojawiło się wiele prac o kratach anihilatorów w algebrach łącznych, oraz o związkach własności tych krat z własnościami krat ideałów jednostronnych i z innymi znanymi, ważnymi własnościami algebr. Celem rozprawy jest kontynuowanie tych badań. Szczególny nacisk jest położony na badanie algebr zredukowanych, oraz algebr półprymarnych, w tym algebr skończenie wymiarowych. Podamy teraz przykłady uzyskanych rezultatów. W rozdziale drugim pokazujemy, że kraty anihilatorów lewostronnych i anihilatorów prawostronnych dowolnej algebry zredukowanej są równe i ta krata jest algebrą Boole
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Ahmadi, Amir. "Axiomatic approach to cellular algebras." Thesis, 2020. http://hdl.handle.net/1866/23949.

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Les algèbres cellulaires furent introduite par J.J. Graham et G.I. Lehrer en 1996. Elles forment une famille d’algèbres associatives de dimension finie définies en termes de « données cellulaires » satisfaisant certains axiomes. Ces données cellulaires, lorsqu’elles sont identifiées pour une certaine algèbre, permettent une construction explicite de tous ses modules simples, à isomorphisme près, et de leurs couvertures projectives. Dans ce mémoire, nous définissons ces algèbres cellulaires en introduisant progressivement chacun des éléments constitutifs d’une façon axiomatique. Deux aut
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Books on the topic "Finite associative algebra"

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Schneider, Peter. Modular Representation Theory of Finite Groups. Springer London, 2013.

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1970-, Iyengar Srikanth, and Krause Henning 1962-, eds. Representations of finite groups: Local cohomology and support. Birkhäuser, 2011.

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Drozd, Yurij A. Finite dimensional algebras. Springer-Verlag, 1994.

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1943-, Wiegand Roger, ed. Cohen-Macaulay representations. American Mathematical Society, 2012.

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editor, Littelmann Peter, ed. Representation theory -- current trends and perspectives. European Mathematical Society Publishing House, 2017.

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Peter, Gabriel. Representations of finite-dimensional algebras. Springer, 1997.

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W, Curtis Charles. Representation theory of finite groups and associative algebras. Wiley, 1988.

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Vlastimil, Dlab, Scott L. L, and Canadian Mathematical Seminar/NATO Advanced Research Workshop (1992 : Carleton University), eds. Finite dimensional algebras and related topics. Kluwer Academic, 1994.

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Igusa, Kiyoshi, 1949- editor of compilation, Martsinkovsky, A. (Alex), editor of compilation, and Todorov, G. (Gordana), editor of compilation, eds. Expository lectures on representation theory: Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA. American Mathematical Society, 2014.

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Session, Ring Theory. Ring theory and its applications: Ring Theory Session in honor of T.Y. Lam on his 70th birthday at the 31st Ohio State-Denison Mathematics Conference, May 25-27, 2012, The Ohio State University, Columbus, OH. Edited by Lam, T. Y. (Tsit-Yuen), 1942- honouree, Huynh, Dinh Van, 1947- editor of compilation, and Ohio State-Denison Mathematics Conference. American Mathematical Society, 2014.

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Book chapters on the topic "Finite associative algebra"

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Eick, Bettina, and Tobias Moede. "Classifying Nilpotent Associative Algebras: Small Coclass and Finite Fields." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_9.

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Prakash, Om, Habibul Islam, and Ram Krishna Verma. "Constacyclic and Skew Constacyclic Codes Over a Finite Commutative Non-chain Ring." In Non-commutative and Non-associative Algebra and Analysis Structures. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-32009-5_26.

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Faith, Carl. "Direct product and sums of rings and modules and the structure of fields." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/01.

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Faith, Carl. "Introduction to ring theory: Schur’s Lemma and semisimple rings, prime and primitive rings, Noetherian and Artinian modules, nil, prime and Jacobson radicals." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/02.

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Faith, Carl. "Direct decompositions of projective and injective modules." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/03.

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Faith, Carl. "Direct product decompositions of von Neumann regular rings and self-injective rings." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/04.

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Faith, Carl. "Direct sums of cyclic modules." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/05.

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Faith, Carl. "When injectives are flat: Coherent FP-injective rings." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/06.

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Faith, Carl. "Direct decompositions and dual generalizations of Noetherian rings." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/07.

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Faith, Carl. "Completely decomposable modules and the Krull-Schmidt-Azumaya theorem." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/08.

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Conference papers on the topic "Finite associative algebra"

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Shlaka, Hasan M., and Durgham A. Mousa. "Inner ideals of the special linear lie algebras of associative simple finite dimensional algebras." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0117506.

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Asses, Mohamed tahar. "TOWARDS QUALITY BUSINESS ENGLISH IN ALGERIA." In eLSE 2014. Editura Universitatii Nationale de Aparare "Carol I", 2014. http://dx.doi.org/10.12753/2066-026x-14-231.

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This workshop highlights the challenges and processes involved in developing Business English teaching competences in a primarily francophone environment. Participants will learn how to fine-tune blended training for trainees with little prior teaching experience. Reference will be made to a British Council--Algerian Chamber of Commerce and Industry project which culminated in setting up quality language centres in Algeria. The purpose of this workshop is to share the "good practices" of the recent Algerian experience in setting up four quality business English language centres that adhere to
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Hettiger, Christof. "Applied Structural Simulation in Railcar Design." In 2017 Joint Rail Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/jrc2017-2330.

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Fifty years ago, the railcar industry relied entirely on classical analysis methods using fundamental solid mechanics theory to establish design and manufacturing protocols. While this method produced working designs, the assumptions required by this type of analysis often led to overdesigned railcars. In the 1950s, the generalized mathematical approach of Finite Element Analysis (FEA) was developed to model the structural behaviors of mechanical systems. FEA involves creating a numerical model by discretizing a continuous system into a finite system of grid divisions. Each grid division, or e
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