Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

The main object of this paper is to study relative homological aspects as well as further
properties of τ-closed submodules. A submodule N of a module M is said to be τ-closed (or τ …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

We call a right module weakly neat-flat if is surjective for any epimorphism and any simple
right ideal. A left module is called weakly absolutely s-pure if is monic, for any …

A module is called coneat injective if it is injective with respect to all coneat exact
sequences. The class of such modules is enveloping and falls properly between injectives …

In the last decade, two new approaches have been introduced for the analysis of the
projectivity of modules. In this paper, the projectivity of modules has been studied with a new …

In this paper, we study left orthogonal class of max-flat modules which are the homological
objects related to s-pure exact sequences of modules and module homomorphisms …

In this survey article, we shall give some properties of classes of short exact sequences of
modules related with complement and supplement submodules; some of them form proper …

A submodule N of a module M is called D D-closed if the socle of M/N is zero. D D-closed
submodules are similar to S S-closed submodules (a generalization of closed submodules) …