Reza Beyranvand, Fatemeh Moradi,
Volume 9, Issue 3 (12-2023)
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.
