Modules Whose Endomorphism Rings are Baer

Abstract

In this paper, we study modules whose endomorphism rings are Baer, which we call endoBaer modules. We provide some characterizations of endoBaer modules and investigate their properties. Some classes of rings R are characterized in terms of endoBaer R-modules. It is shown that a direct summand of an endoBaer modules inherits the property, while a direct sum of endoBaer modules does not. Necessary and sucient conditions for a nite direct sum of endoBaer modules to be an endoBaer module are provided.