One proof of the original Kemer's theorems (concerning the text of C. Procesi "What happened to PI-theory", arxiv.org/abs/1403.5673)

2015/03/12 by Sviridova, Irina
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1503.03574

Abstract

We consider associative algebras over a field of characteristic zero. We give a version of the proof of the Kemer's theorems concerning the Specht problem solution. It is proved that the ideal of graded identities of a finitely generated PI-superalgebra coincides with the ideal of graded identities of some finite dimensional superalgebra. This implies that the ideal of polynomial identities of any (not necessary finitely generated) PI-algebra coincides with the ideal of identities of the Grassmann envelope of a finite dimensional superalgebra, and is finitely generated as a T-ideal.

Related

• Kemer's Theory for H-Module Algebras with Application to the PI Exponent
• Finite basis problem for identities with involution
• Identities of finitely generated graded algebras with involution
• On sums of gr-PI algebras
• Superpolynomial identities of finite-dimensional simple algebras