Central polynomials for matrix algebras over the Grassmann algebra

Abstract

Abstract. In this work, we describe a method to construct central polynomials for F -algebras where F is a field of characteristic zero. The main application deals with the T -prime algebras Mn(E), where E is the infinite-dimensional Grassmann algebra over F , which play a fundamental role in the theory of PI-algebras. The method is based on the explicit decomposition of the group algebra F Sn.