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: 7 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 algebra with an involution, all derived powers of [Formula: see text] are finitely generated Lie algebras.
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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 of Amitsur's conjecture for graded polynomial identities of finite-dimensional associative algebras over a field of characteristic 0, graded by any group. In addition, we provide a criterion for graded simplicity of an associative algebra in terms of graded codimensions.
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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 embeddings between quivers, incidence algebras and other structures which relate indecomposable representations of algebras and some subalgebras via induction/restriction functors. Some results in literature are also re-derived as a particular case, and other applications are given.
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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 action of a semigroup by anti-endomorphisms). This approach proves to be especially fruitful in the theory of polynomial identities. We show that if [Formula: see text] is a finite dimensional (not necessarily associative) algebra over a field of characteristic [Formula: see text] and [Formula: see text] is simple with respect to a generalized [Formula: see text]-action, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of polynomial [Formula: see text]-identities of [Formula: see text]. In particular, if [Formula: see text] is a finite dimensional (not necessarily group graded) graded-simple algebra, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of graded polynomial identities of [Formula: see text]. In addition, we study the free-forgetful adjunctions corresponding to (not necessarily group) gradings and generalized [Formula: see text]-actions.
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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 associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided.
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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 can be reduced to discrete logarithm in the finite field that is an extension of the field over which the quaternion algebra is defined. Therefore further investigations of the congruent logarithm problem as primitive of the post-quantum cryptoschemes should be carried out in direction of finding new its carriers. The present paper introduces novel associative algebras possessing significantly different properties than quaternion algebra, in particular they contain no global unit. This difference had demanded a new definition of the discrete logarithm problem in a hidden group, which is different from the congruent logarithm. There are proposed several variants of such definition, in which it is used the notion of the local unite. There are considered right, left, and bi-side local unites. Two general methods for constructing the finite associative algebras with non-commutative multiplication operation are proposed. The first method relates to defining the algebras having dimension value equal to a natural number m > 1, and the second one relates to defining the algebras having arbitrary even dimensions. For the first time the digital signature algorithms based on computational difficulty of the discrete logarithm problem in a hidden group have been proposed.
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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 stable equivalences and transferring gradings via derived equivalences. The main idea that we use is the following. We start with an algebra which can be easily graded, and transfer this grading via derived or stable equivalence to another algebra which is not easily graded. We investigate the properties of the resulting grading. In the first chapter we list the background results that will be used in this thesis. In the second chapter we study gradings on Brauer tree algebras, a class of algebras that contains blocks of group algebras with cyclic defect groups. We show that there is a unique grading up to graded Morita equivalence and rescaling on an arbitrary basic Brauer tree algebra. The third chapter is devoted to the study of gradings on tame blocks of group algebras. We study extensively the class of blocks with dihedral defect groups. We investigate the existence, positivity and tightness of gradings, and we classify all gradings on these blocks up to graded Morita equivalence. The last chapter deals with the problem of transferring gradings via stable equivalences between blocks of group algebras. We demonstrate on three examples how such a transfer via stable equivalences is achieved between Brauer correspondents, where the group in question is a TI group.
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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(-) and A(k) = [A(k-1),A(k-1)] for all k ≥ 1. Let L be the Lie algebra A(k) (k ≥ 0). In the first half of this thesis, we prove that every Jordan-Lie inner ideal of L admits Levi decomposition. We get full classification of Jordan-Lie inner ideals of L satisfying a certain minimality condition. In the second half of this thesis, we study Jordan-Lie inner ideals of Lie subalgebras of finite dimensional associative algebras with involution. Let A be a finite dimensional associative algebra over F with involution * and let K(1) be the derived Lie subalgebra of the Lie algebra K of the skew-symmetric elements of A with respect to *. We classify * -regular inner ideals of K and K(1) satisfying a certain minimality condition and show that every bar-minimal * -regular inner ideal of K or K(1) is of the form eKe* for some idempotent e in A with e*e = 0. Finally, we study Jordan-Lie inner ideals of K(1) in the case when A does not have “small” quotients and show that they admit *-invariant Levi decomposition.
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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 case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.
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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 algebras. Necessary and sufficient conditions for finite generation of the Hochschild cohomology ring modulo nilpotent elements for a partly (anti-)commutative Koszul quiver algebra are given.
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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 alors que si deux paires sont équivalentes, alors les W-algèbres associées sont isomorphes. Nous introduisons enfin les notions de graduation et paire admissibles b-maximales et nous montrons que les paires admissibles b-maximales sont équivalentes entre elles. Comme conséquence de ce résultat, nous retrouvons un résultat de Brundan et Goodwin sur les bonnes graduations. Dans une dernière partie, nous considérons des cas particuliers pour lesquels nous pouvons apporter une réponse complète à la question d'isomorphisme<br>Let g be a complex simple Lie algebra and e a nilpotent element of g. We are interested to answer the isomorphism question (raised by Premet) between the finite W-algebras constructed from some nilpotent subalgebras of g called e-admissible. We introduce the concept of e-admissible pair and e-admissible grading. We show then that the W-algebra associated to an e-admissible pair admits similar properties to that introduced by Gan and Ginzburg. Moreover, we define an equivalence relation on the set of admissible pairs and we show that if two admissible pairs are equivalent, it follows that the associated W-algebras are isomorphic. We introduce later the concepts of b-maximal admissible pair and b-maximal admissible grading and show that b-maximal admissible pairs are equivalent. As a consequence to this result, we recover a result of Brundan and Goodwin on the good gradings. In a final part, we consider some particular cases where we may find a complete answer to the isomorphism question
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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'a. Jeśli A jest algebrą półprymarną, to krata anihilatorów tej algebry jest algebrą Boole'a wtedy i tylko wtedy, gdy A jest skończoną sumą prostą algebr z dzieleniem. W rozdziale trzecim, dla dowolnego ciała K i dla dowolnej kraty L konstruujemy lokalną algebrę K[L], taką że jej krata anihilatorów zawiera L jako podkratę. Można przy tym żądać, aby algebra K[L] była przemienna. To pozwala nam udowodnić, że nie istnieje żadna nietrywialna tożsamość spełniona w kratach anihilatorów wszystkich algebr lokalnych. Przypomnijmy, że kraty ideałów jednostronnych we wszystkich algebrach są modularne, a więc spełniają wiele wspólnych, nietrywialnych tożsamości. Jeśli L jest kratą skończoną, to nasza algebra K[L] jest skończenie wymiarowa. Tak więc otrzymujemy przykłady zanurzeń krat skończonych w kraty anihilatorów algebr skończenie wymiarowych, nawet dla tych krat, dla których wcześniej znane były zanurzenia jedynie w kraty anihilatorów algebr nieskończenie wymiarowych. Korzystając ze wspomnianej wyżej konstrukcji opisujemy, w rozdziale czwartym, kraty skończone, które mogą być reprezentowane jako kraty wszystkich anihilatorów algebr skończenie wymiarowych nad ciałami nieskończonymi.<br>In several papers connections of properties of lattices of annihilators with properties of lattices of one-sided ideals and with other important properties of associative algebras are considered. The aim of this dissertation is to continue these considerations. Special attention will be paid to reduced algebras and semiprimary algebras, in particular to finite dimensional algebras. We provide now some of obtained results. In chapter two we show that for every reduced algebra the lattices of its left annihilators and right annihilators are equal and this lattice is a Boolean algebra. If A is a semiprimary algebra, then the lattices of annihilators of A are Boolean algebras if and only if A is a finite direct sum of division algebras. In the third chapter, for any field K and for arbitrary lattice L we construct a local algebra K[L] and a lattice embedding of L into the lattice of left annihilators of K[L]. In addition we can assume, that K[L] is a commutative algebra. As a consequence, we are able to prove that there is no nontrivial identity satisfied in all lattices of annihilators in local algebras. Let us remind, that lattices of one-sided ideals in all algebras are modular. Thus they satisfy many nontrivial identities. If L is a finite lattice, then our algebra K[L] is finite dimensional. Hence we obtain an embedding of any finite lattice into a lattice of annihilators in a finite dimensional algebra. Earlier examples from the literature showed mainly embeddings into lattices of annihilators of infinite dimensional algebras. Using our construction we also describe, in chapter four, finite lattices being representable as lattices of all annihilators in finite dimensional algebras over infinite fields.
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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 autres familles d’algèbres associatives sont discutées, à savoir les algèbres quasihéréditaires et celles dont les modules forment une catégorie de plus haut poids. Ces familles furent introduites durant la même période de temps, au tournant des années quatre-vingtdix. La relation entre ces deux familles ainsi que celle entre elles et les algèbres cellulaires sont prouvées.<br>Cellular algebras were introduced by J.J. Graham and G.I. Lehrer in 1996. They are a class of finite-dimensional associative algebras defined in terms of a “cellular datum” satisfying some axioms. This cellular datum, when made explicit for a given associative algebra, allows for the explicit construction of all its simple modules, up to isomorphism, and of their projective covers. In this work, we define these cellular algebras by introducing each building block of the cellular datum in a fairly axiomatic fashion. Two other families of associative algebras are discussed, namely the quasi-hereditary algebras and those whose modules form a highest weight category. These families were introduced at about the same period. The relationships between these two, and between them and the cellular ones, are made explicit.
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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 international norms and standards. The focus will be on the three blended teacher and trainer training phases of the project that were managed by the Algerian chamber of commerce and Industry with the help of British Council Algeria, experienced LCCI (London Chamber of Commerce and Industry) trainers and the Algerian Quality Association for Language Services (AQuALS). Whether experienced or inexperienced business English teachers, teacher trainers or academic managers; participants will find the hands-on approaches and field-tested instruments of great use in contexts with similar challenges. The talk starts with an examination of the context of business English language learning and teaching and factors that slowed down progress towards quality education in the country. Then, it describes the above project that was launched to meet the need for quality and standards. Next, it delineates the thematic and key professional skills that were covered, the adopted approaches and the challenges in the teacher/trainer training and development stages of the project. As one of the main project facilitators, the presenter will share the learned lessons with the participants and explores the mechanisms, instruments, strategies and peer support systems that were used to ensure quality. Last but not least, the participants' questions and comments during the last ten minutes will enable the presenter to shed more light on areas of their interest.
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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 element, has an inherent geometric shape and each element is comprised of points which are referred to as nodes. The connected pattern of nodes and elements is called a mesh. A solver organizes the mesh into a matrix of differential equations and computes the displacements using linear algebraic operations from which strains and stresses are obtained. The rapid development of computing technology provided the catalyst to drive FEA from research into industry. FEA is currently the standard approach for improving product design cycle times that were previously achieved by trial and error. Moreover, simulation has improved design efficiency allowing for greater advances in weight, strength, and material optimization. While FEA had its roots planted in the aerospace industry, competitive market conditions have driven simulation into many other professional fields of engineering. For the last few decades, FEA has become essential to the submittal of new railcar designs for unrestricted interchange service across North America. All new railcar designs must be compliant to a list of structural requirements mandated by the Association of American Railroads (AAR), which are listed in its MSRP (Manual of Standards and Recommended Practices) in addition to recommended practices in Finite Element (FE) modeling procedures. The MSRP recognizes that these guidelines are not always feasible to completely simulate, allowing the analyst to justify situations where deviations are necessary. Benefits notwithstanding, FEA has inherent challenges. It is understood that FEA does not provide exact solutions, only approximations. While FEA can provide meaningful insight into actual physical behavior leading to shorter development times and lower costs, it can also create bogus solutions that lead to potential safety and engineering risks. Regardless of how appropriate the FEA assumptions may be, engineering judgment is required to interpret the accuracy and significance of the results. A constant balance is made between model fidelity and computational solve time. The purpose of this paper is to discuss the FEA approach to railcar analysis that is used by BNSF Logistics, LLC (BNSFL) in creating AAR compliant railcar designs. Additionally, this paper will discuss the challenges inherent to FEA using experiences from actual case studies in the railcar industry. These challenges originate from assumptions that are made for the analysis including element types, part connections, and constraint locations for the model. All FEA terminology discussed in this paper is written from the perspective of an ANSYS Mechanical user. Closing remarks will be given about where current advances in FEA technology may be able to further improve railcar industry standards.
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