Finite basis problem for identities with involution

Abstract

We consider associative algebras with involution over a field of characteristic zero. We proved that any algebra with involution satisfies the same identities with involution as the Grassmann envelope of some finite dimensional $Z_4$-graded algebra with graded involution. As a consequence we obtain the positive solution of the Specht problem for identities with involution: any associative algebra with involution over a field of characteristic zero has a finite basis of identities with involution. These results are analogs of theorems of A.R.Kemer for ordinary identities.

References in corpus (1)

• Identities of finitely generated graded algebras with involution

Cited by in corpus (1)

• Polynomial identities with involution for the algebra of 3 $\times$ 3 upper triangular matrices