On Simple Finite-Dimensional Algebras with Infinite Basis of Identities

A. V. Kislitsin

Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 753-758.

Résumé

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.

Détail

Keywords: central algebra, simple algebra, identity of an algebra, basis of identities, nonfinitely based algebra.

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