Identities of PI-Algebras Graded by a Finite Abelian Group

Group graded algebras and almost polynomial growth

“…A basic theorem that we shall need in the sequel is the following result proved independently by Aljadeff-Belov in [1] and Sviridova in [19]. We should point out that this theorem was proved in [1] for non-necessarily abelian groups.…”

“…We first recall that if A is a G × Z 2 -graded algebra, then the Grassmann envelope of A is ,i) is the decomposition of A into its homogeneous components. [1,19].) Let A be a G-graded algebra satisfying an ordinary polynomial identity.…”

“…We shall also make use of a basic result recently proved independently by Aljadeff-Belov [1] and Sviridova [19] allowing us to reduce our problem to the study of the Grassmann envelope of a finite dimensional G × Z 2 -graded algebra.…”

Group graded algebras and multiplicities bounded by a constant

“…Next we recall a very useful theorem of Aljadeff and Kanel-Belov [3], proved independently by Sviridova in [15] for abelian groups.…”

Kemer's theory for H-module algebras with application to the PI exponent

“…In all of these frameworks analogs of these problems exist and in some of them also solved: For finite group-graded algebras satisfying an ordinary PI see [3] (it is worth mentioning that in [15] the special case of abilean finite groups is treated). For algebras with involutions satisfying an ordinary PI see [16].…”