ON RINGS ALL OF WHOSE MODULES ARE RETRACTABLE

Abstract

Let R be a ring. A right R-module M is said to be retractable if Hom(R) (M, N) not equal 0 whenever N is a non-zero submodule of M. The goal of this article is to investigate a ring R for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that (1) The ring Pi(i is an element of I) R-i is right mod-retractable if and only if each R-i is a right mod-retractable ring for each i is an element of I, where I is an arbitrary finite set. (2) If R[x] is a mod-retractable ring then R is a mod-retractable ring.