Endoregular Modules

Abstract

We will discuss modules whose endomorphism rings are von Neumann regular, which we call endoregular modules. Characterizations and properties of endoregular modules will be presented. For example, it is shown that a direct summand of an endoregular module inherits the property, while a direct sum of endoregular modules does not. Necessary and sufficient conditions for a finite direct sum of endoregular modules to be an endoregular module will be discussed. As a special case, modules whose endomorphism rings are semisimple artinian are characterized.