| Abstract: | Abstract Let 𝕂 be a field of characteristic zero, and R be a G-graded 𝕂-algebra. We consider the algebra R ? E, then deduce its G × ?2-graded polynomial identities starting from the G-graded polynomial identities of R. As a consequence, we describe a basis for the ? n × ?2-graded identities of the algebras M n (E). Moreover we give the graded cocharacter sequence of M 2(E), and show that M 2(E) is PI-equivalent to M 1,1(E) ? E. This fact is a particular case of a more general result obtained by Kemer. |
