Modules Whose Endomorphism Rings are Baer
Thoraya Abdelwhab
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu, P.R. China and Faculty of Mathematical Sciences, University of Khartoum, Khartoum, Khartoum, Sudan.
Xiaoyan Yang *
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu, P.R. China.
*Author to whom correspondence should be addressed.
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.
Keywords: Baer module, endoBaer module, Rickart module, Rickart ring, Baer ring.