In 1993 I. P. Shestakov came up with the question whether there exists a central simple finite-dimensional algebra over a field of characteristic 0, whose identities are not given by a finite set (Dniester Notebook, Question 3.103). In 2012 I. M. Isaev and the author constructed a desired example, giving an affirmative answer to the question posed. Here research into Shestakov’s question is continued for the case of commutative algebras. A seven-dimensional central simple commutative algebra over a field of characteristics 0 having no finite basis of identities is exemplified.
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Translated from Algebra i Logika, Vol. 54, No. 3, pp. 315-325, May-June, 2015.
*Supported by the Russian Ministry of Education and Science, gov. contract No. 2014/418.
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Kislitsin, A.V. An Example of a Central Simple Commutative Finite-Dimensional Algebra with an Infinite Basis of Identities. Algebra Logic 54, 204–210 (2015). https://doi.org/10.1007/s10469-015-9341-x
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DOI: https://doi.org/10.1007/s10469-015-9341-x