THE ALGEBRA GENERATED BY NILPOTENT ELEMENTS IN A MATRIX CENTRALIZER

Abstract

For an arbitrary square matrix S, denote by C(S) the centralizer of S, and by C(S)N the set of all nilpotent elements in C(S). In this paper, we use the Weyr canonical form to study the subalgebra of C(S) generated by C(S)N. We determine conditions on S such that C(S)N is a subalgebra of C(S). We also determine conditions on S such that the subal-gebra generated by C(S)N is C(S).