Identities of semigroup algebras of completely O-simple semigroups

Abstract

Let H = M0(G; I, Λ; P) be a Rees semigroup of matrix type with sandwich matrix P over a group H0 with zero. If F is a subgroup of G of finite index and X is a system of representatives of the left cosets of F in G, then with the matrix P there is associated in a natural way a matrix P(F, X) over the group F0 with zero. Our main result: the semigroup algebra K[H] of H over a field K of characteristic 0 satisfies an identity if and only if G has an Abelian subgroup F of finite index and, for any X, the matrix P(F, X) has finite determinant rank.