Geodesic
On Simple Finite-Dimensional Algebras with Infinite Basis of Identities
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 753-758

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: central algebra, simple algebra, identity of an algebra, basis of identities, nonfinitely based algebra. 
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     author = {A. V. Kislitsin},
     title = {On {Simple} {Finite-Dimensional} {Algebras} with {Infinite} {Basis} of {Identities}},
     journal = {Matemati\v{c}eskie zametki},
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A. V. Kislitsin. On Simple Finite-Dimensional Algebras with Infinite Basis of Identities. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 753-758. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a7/