Grassmann algebras over finite fields

Abstract

We study an analogue of a problem of procesi about matrices [9, page 185(e)]: are there non-trivial polynomials over Z which become identities over Z p - for grassmann algebras E? when 1 ∊ E, we show that such polynomials do not exist, but when 1 ∉,E such polynomials exist - also for matrices over E. these results are deduced from a careful study of the various codimensions of these algebras.