Email this article Modules close to SSP- and SIP-modules
- Authors: Abyzov A.N.1, Nhan T.H.2, Quynh T.C.3
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Affiliations:
- Department of Algebra and Mathematical Logic
- Department of IT and Mathematics Teacher Training
- Department of Mathematics
- Issue: Vol 38, No 1 (2017)
- Pages: 16-23
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198588
- DOI: https://doi.org/10.1134/S1995080217010024
- ID: 198588
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Abstract
In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that R is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover. We also prove that R is a semiregular ring and J(R) = Z(RR) if only if every finitely generated projective module is a CSRickart module which is also a C2 module.
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About the authors
A. N. Abyzov
Department of Algebra and Mathematical Logic
Author for correspondence.
Email: Adel.Abyzov@ksu.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, 420008
Tran Hoai Ngoc Nhan
Department of IT and Mathematics Teacher Training
Email: Adel.Abyzov@ksu.ru
Viet Nam, Cao Lãnh
Truong Cong Quynh
Department of Mathematics
Email: Adel.Abyzov@ksu.ru
Viet Nam, 459 Ton Duc Thang, Danang city
