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Communications in Algebra Volume 39, 2011 - Issue 3
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Original Articles

Polynomial Identities of Finite Dimensional Simple Algebras

Ivan Shestakov Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, BrasilCorrespondence[email protected]
&
Mikhail Zaicev Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia
Pages 929-932 | Received 31 Oct 2009, Published online: 16 Mar 2011

Citations (18)

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I.M. Isaev & A.V. Kislitsin. (2013) Example of Simple Finite Dimensional Algebra with No Finite Basis of Its Identities. Communications in Algebra 41:12, pages 4593-4601.
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Articles from other publishers (17)

Diogo Diniz, Dimas José Gonçalves, Viviane Ribeiro Tomaz da Silva & Manuela da Silva Souza. (2024) The isomorphism problem in the context of PI-theory for two-dimensional Jordan algebras. Finite Fields and Their Applications 94, pages 102344.
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A. V. Kislitsin. (2024) On Simple Finite-Dimensional Algebras with Infinite Basis of Identities. Mathematical Notes 114:5-6, pages 845-849.
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Alexey Vladimirovich Kislitsin. (2023) О простых конечномерных алгебрах с бесконечными базисами тождествOn Simple Finite-Dimensional Algebras with Infinite Bases of Identities. Математические заметки Matematicheskie Zametki 114:5, pages 753-758.
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L. S. I. Murakami, L. A. Peresi & I. P. Shestakov. (2021) A retrospect of the research in nonassociative algebras in IME-USP. São Paulo Journal of Mathematical Sciences 16:1, pages 84-130.
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Waldeck Schützer & Abel Gomes de Oliveira. (2020) On some H-Galois objects and their polynomial H-identities. Archiv der Mathematik 116:1, pages 7-18.
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Yuri Bahturin & Felipe Yasumura. (2019) Distinguishing simple algebras by means of polynomial identities. São Paulo Journal of Mathematical Sciences 13:1, pages 39-72.
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Angelo Bianchi & Diogo Diniz. (2019) Identities and isomorphisms of finite-dimensional graded simple algebras. Journal of Algebra 526, pages 333-344.
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Yuri Bahturin & Felipe Yasumura. (2019) Graded polynomial identities as identities of universal algebras. Linear Algebra and its Applications 562, pages 1-14.
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Fernando Henry. (2018) Some graded identities of the Cayley–Dickson algebra. International Journal of Algebra and Computation 28:05, pages 697-718.
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Yuri Bahturin & Diogo Diniz. (2018) Graded identities of simple real graded division algebras. Journal of Algebra 500, pages 316-334.
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A. V. Kislitsin. (2017) Simple finite-dimensional algebras without finite basis of identities. Siberian Mathematical Journal 58:3, pages 461-466.
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Onofrio Mario Di Vincenzo & Ernesto Spinelli. (2015) Minimal varieties of associative PI (super)-algebras with respect to their (graded) exponent. São Paulo Journal of Mathematical Sciences 10:2, pages 248-262.
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A. V. Kislitsin. (2015) An Example of a Central Simple Commutative Finite-Dimensional Algebra with an Infinite Basis of Identities. Algebra and Logic 54:3, pages 204-210.
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Onofrio Mario Di Vincenzo & Ernesto Spinelli. (2014) Graded polynomial identities on upper block triangular matrix algebras. Journal of Algebra 415, pages 50-64.
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Eli Aljadeff & Darrell Haile. (2013) Simple 𝐺-graded algebras and their polynomial identities. Transactions of the American Mathematical Society 366:4, pages 1749-1771.
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Pasha Zusmanovich. (2013) On the utility of Robinson–Amitsur ultrafilters. Journal of Algebra 388, pages 268-286.
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I. M. Isaev & A. V. Kislitsin. (2013) An example of a simple finite-dimensional algebra with no finite basis of identities. Doklady Mathematics 86:3, pages 774-775.
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