Modules Whose Endomorphism Rings are Right Rickart

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Thoraya Abdelwhab
Xiaoyan Yang

Abstract

In this paper, we study modules whose endomorphism rings are right Rickart (or right p.p.) rings, which we call R-endoRickart modules. We provide some characterizations of R-endoRickart modules. Some classes of rings are characterized in terms of R-endoRickart modules. We prove that an R-endoRickart module with no innite set of nonzero orthogonal idempotents in its endomorphism ring is precisely an endoBaer module. We show that a direct summand of an R-endoRickart modules inherits the property, while a direct sum of R-endoRickart modules does not. Necessary and sucient conditions for a nite direct sum of R-endoRickart modules to be an R-endoRickart module are provided.

Keywords:
R-endoRickart module, endoBaer module, Rickart module, right Rickart ring, Baer ring.

Article Details

How to Cite
Abdelwhab, T., & Yang, X. (2019). Modules Whose Endomorphism Rings are Right Rickart. Asian Research Journal of Mathematics, 13(2), 1-14. https://doi.org/10.9734/arjom/2019/v13i230101
Section
Review Article