Volume 9, Issue 3 (12-2023)                   mmr 2023, 9(3): 1-20 | Back to browse issues page

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beyranvand R, moradi F. A generalization of retractable modules. mmr 2023; 9 (3) :1-20
URL: http://mmr.khu.ac.ir/article-1-3240-en.html
A generalization of retractable modules
Reza Beyranvand * 1, Fatemeh Moradi2
1- lorestan university , beyranvand.r@lu.ac.ir
2- lorestan university
Abstract:   (918 Views)
Let R be an arbitrary ring and N be a right R-module.  A right R-module M is called N-retractable if HomR(M,N')≠0, for any nonzero submodule N' of N. This is a generalization of the concept of retractable modules. The aim of this paper is to study of N-retractable modules, where N is an arbitrary right R-module. One of the most important results of this paper is the characterization of rings that have a module such that each module is retractable with respect to it. Also we show that the class of N-retractable modules is closed under direct sums and direct products.   
Keywords: retractable module, singular module, nonsingular module
Full-Text [PDF 1443 kb]   (441 Downloads)    
Type of Study: S | Subject: alg
Received: 2021/11/1 | Revised: 2024/03/2 | Accepted: 2022/04/22 | Published: 2023/12/5 | ePublished: 2023/12/5
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