Graded Identities of Several Tensor Products of the Grassmann Algebra.

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 E_gr an arbitrary ℤ 2 -grading on E such that the subspace L is homogeneous. We consider E_gr ⊗ E^⊗n as a (ℤ 2 × 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. [ABSTRACT FROM AUTHOR]