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

We investigate the structure of semi-centralizing and kcommuting 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.