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On Simple Finite-Dimensional Algebras with Infinite Basis of Identities

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Abstract

In 1993, I. P. Shestakov posed the question of the existence of a central simple finite-dimensional algebra over a field of characteristic zero whose identities are not given by a finite set of identities. In 2012, I. M. Isaev and the author of the present paper constructed an example of a seven-dimensional central simple algebra over any field that does not have a finite basis of identities. In the present paper, we construct an example of a six-dimensional central simple algebra over a field of characteristic zero which has no finite basis of identities.

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Funding

This work was financially supported by the Russian Science Foundation, project 22-21-00745, https://rscf.ru/en/project/22-21-00745/.

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Authors and Affiliations

  1. Omsk State University, Omsk, 644077, Russia

    A. V. Kislitsin

  2. Altai State Pedagogical University, Barnaul, 656031, Russia

    A. V. Kislitsin

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  1. A. V. Kislitsin
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Correspondence to A. V. Kislitsin.

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Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 753–758 https://doi.org/10.4213/mzm14057.

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Kislitsin, A.V. On Simple Finite-Dimensional Algebras with Infinite Basis of Identities. Math Notes 114, 845–849 (2023). https://doi.org/10.1134/S0001434623110196

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