Let R be a commutative ring. A finitely generated R-module M can be converted into an R
[X]− module by an R− endomorphism of M (see for example [4]). In this work, we first give a …

It is well-known that a right self-injective, left go-injective regular ring is directly finite, and
then unit-regular (cf.[2, Theorem 9.29].) Also, it is proved in [3, Theorem 1.8] that a right go …

This paper introduce and investigate the notion of FI− M− principally injective and FI− semi-
injective (fully invariant-semi injective) modules. Clearly FI− semi-injective module does not …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Every indecomposable module over a generalized uniserial ring is uniserial, hence local.
This motivates one to study rings R satisfying the condition (*): R is a right artinian ring such …

We investigate characterizations of rings whose simple singular right R-modules are GP-
injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

This note contains the following results for a ring A:(1) A is von Neumann regular if, and only
if, every divisible singular left A-module is pinjective and every p-injective left A-module is …

Let R be a commutative unital ring and E a unital R-module. Then the canonical injective
ring homomorphism from R into the idealization R (+) E is a minimal ring homomorphism if …

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 …