Abdelwhab, Thoraya and Yang, Xiaoyan (2019) Modules Whose Endomorphism Rings are Right Rickart. Asian Research Journal of Mathematics, 13 (2). pp. 1-14. ISSN 2456-477X
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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.
Item Type: | Article |
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Subjects: | Open STM Article > Mathematical Science |
Depositing User: | Unnamed user with email support@openstmarticle.com |
Date Deposited: | 11 May 2023 07:26 |
Last Modified: | 20 Jul 2024 09:38 |
URI: | http://asian.openbookpublished.com/id/eprint/493 |