The basis of the graded polynomial identities for superalgebras of triangular matrices

Abstract

Let R' and R'' be associative algebras over a field and let M be a free R'—R''-bimodule. We find a basis of the Z 2-graded polynomial identities for the superalgebra of 2 × 2 x 2 upper triangular matrices with the canonical Z 2 -grading , assuming that we know the bases of the T-ideals T(R'),T(R''), T(R') ⋂ T(R'') of the ordinary polynomial identities for the algebras R', R'' and R' + R'' respectively. We also apply this result in order to find bases for the superidentities of some matrix algebras.