An Example of a Central Simple Commutative Finite-Dimensional Algebra with an Infinite Basis of Identities

Abstract

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.