ABSTRACT A widely used result of Wedderburn and Artin states that “every left ideal of a
ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct …

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image
of M. It is shown that if R is a right perfect ring, then every projective slightly compressible …

Modules in which every submodule is isomorphic to a direct summand is called virtually
semisimple. In this article, we carry out a study of virtually semisimple modules over a …

In this paper, we introduce the notion of t-epi-modules. An R-module M is called t-epi if every
t-closed submodule of M is a homomorphic image of M. Various properties of these modules …

A module M is called co-epi-retractable if it contains a copy of each of its factor modules. It is
proved that a ring R is co-pri (ie, RR is co-epi-retractable) and reduced if and only if R is a …

We say that an R-module M satisfies epi-ACC on submodules if in every ascending chain of
submodules of M, except probably a finite number, each module in chain is a homomorphic …

A new generalizations of retractable modules relative to a submodule are introduced where
a module Script M is called retractable module relative to a submodule N of M if for all non …

In this paper we study M-small principally injective (in short, M-sp-injective) module which is
the generalization of M-principally injective module. We prove that if M is finite dimensional …

Let $ R $ be an arbitrary ring with identity and $ M $ a right $ R $-module with $ S= $ End $
_R (M) $. In this paper we introduce $\pi $-Rickart modules as a generalization of Rickart …

We study rings whose modules and module homomorphisms display behavior similar to that
of sets and their maps. For example, whenever there is an epimorphism A→ B, there is a …