Example of Simple Finite Dimensional Algebra with No Finite Basis of Its Identities

Abstract In 1993, I. P. Shestakov formulated the following question: Are there finite dimensional central simple algebras over a field of characteristic 0 that do not have a finite basis of identities (Dniester notebook, question 3.103)? In this paper, the authors give the positive answer to Shestakov's question. ACKNOWLEDGMENT Authors express deep appreciation to Prof. Yu. N. Maltsev and Prof. I. P. Shestakov for their attention to the paper and for helpful remarks. The work is partially supported by RFBR (project 12.01.00329a) and by RF Ministry of Education and Science via project 1.4311.2011. Notes Communicated by I. Shestakov.

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