Z2-graded identities of the Grassmann algebra in positive characteristic

Let F be an infinite field of characteristic p>2 and let E be the Grassmann algebra generated by an infinite dimensional vector space V over F. In this paper, we describe the T2-ideal of the Z2-graded polynomial identities of the Grassmann algebra E for any Z2-grading such that V is homogeneous in the grading. In particular, we give a description of the T2-ideal of the graded identities of E in the case there is a finite number of homogeneous elements of the linear basis of E belonging to one of the homogenous components of E. © 2011 Elsevier Inc. All rights reserved.