Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

Let M and N be R-modules. We define where S denotes the class of all M-small modules.
We call N an M-cosingular (non-M-cosingular) module if ZM (N)= 0 (ZM (N)= N). We study …

Let R be a ring and M a right R-module. It is shown that:(1) M is Artinian if and only if M is a
GAS-module and satisfies DCC on generalized supplement submodules and on small …

In this paper, δ-lifting and δ-supplemented modules are defined as generalizations of lifting
and supplemented modules. Several properties of these modules are proved. New …

ABSTRACT PF Smith studied modules in which every submodule has a unique closure and
called them UC modules. In this paper we consider modules with the dual property viz …

Let $ R $ be any ring and let $ M $ be any right $ R $-module. $ M $ is called hollow-lifting if
every submodule $ N $ of $ M $ such that $ M/N $ is hollow has a coessential submodule …

We prove that a module M is cofinitely weak supplemented or briefly cws (ie, every
submodule N of M with M/N finitely generated, has a weak supplement) if and only if every …

Let R be an associative ring with identity and let M be a unitary left R–module. As a
generalization of small submodule, we introduce Jacobson–small submodule (briefly J …

The notion of⊕-supplemented modules is a proper generalization of lifting modules. As a
proper generalization of⊕-supplemented modules, we introduce (D 12)-modules and obtain …

Harada (cf.) introduced the lifting property for maximal submodules and the extending
property for simple submodules, and Oshiro (cf.) definitely introduced lifting modules and …