Semi Centralizing Maps and K-Commuting Maps of Module Extension Algebras

Abstract

We investigate the structure of semi-centralizing and k-commuting maps of
module extension algebras. In particular, we give conditions that every semi-centralizing
and k-commuting map L of such an algebra is of the form L(c) = cx+h(c), where x lies
in the center of the algebra and h is a linear map from the algebra to its center.