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.
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