A generalization of retractable modules

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Moradi Fatemeh; Beyranvand Reza

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Journal Paper

Paper Information

Journal: Mathematical Researches Year:2023 | Volume:9 | Issue:3 Page(s): 1-20

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Information Journal Paper

Title

A generalization of retractable modules

Author(s)

Moradi Fatemeh | Beyranvand Reza | Issue Writer Certificate

Keywords

retractable module

singular module

nonsingular module

Abstract

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.

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