Graded Identities of Several Tensor Products of the Grassmann Algebra

Abstract

Let F be an infinite field of characteristic different from two and E be the unitary Grassmann algebra of an infinite dimensional F-vector space L. Denote by Egr an arbitrary $\mathbb {Z}_{2}$ -grading on E such that the subspace L is homogeneous. We consider Egr ⊗ E⊗n as a $(\mathbb {Z}_{2}\times {\mathbb {Z}_{2}^{n}})$ -graded algebra, where the grading on E is supposed to be the canonical one, and we find its graded ideal of identities.