Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

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

A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

A module is extending (or CS, C1) if every complement submodule is a direct summand or,
equivalently, every submodule is essential in a direct summand. The terms extending and …

In this article, we define a module M to be 𝒢-extending if and only if for each X≤ M there
exists a direct summand D of M such that X∩ D is essential in both X and D. We consider …

A module is extending (or has the property (Q)) if every complement submodule is a direct
summand. We prove that a module over a commutative domain has this property, if and only …

We have defined aconcept of almost M-projectives and almost M-injectives in [4] and [9],
respectively. In the first section of this paper we give some relations among lifting modules …

Let R be a ring and let M= M•© M2 be a right R-module which is the direct sum of
submodules M•, M2. We are interested in conditions on M•, M2 which make M a CS-module …

Weak as-modules share some of the properties of as-modules. For example, we prove that if
M is a weak CS-module which satisfies the ascending chain condition on essential …

A module is extending (or a CS-module, or a module with if every submodule is essential in
a direct summand (equivalen tly, if every closed submodule is a direct summand). Extending …