In this article, we introduce the notion of M-coidempotent elements of a ring and investigate
their connections with fully coidempotent modules, fully copure modules and vn-regular …

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 …

The concept of weak relative-injectivity of modules was introduced in [6] in order to study
rings all of whose cyclic modules are embeddable as essential submodules of projective …

We develop a technique to construct finitely injective modules which are non-trivial, in the
sense that they are not direct sums of injective modules. As a consequence, we prove that a …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

An $ R $-module $ M $ is called virtually uniserial if for every finitely generated submodule
$0\neq K\subseteq M $, $ K/$ Rad $(K) $ is virtually simple. In this paper, we generalize …

Let R be a commutative Noetherian ring, I an ideal of R and let M and N be non-zero R-
modules. It is shown that the R-modules ExtRi (N, M) are I-cofinite, for all i⩾ 0, whenever M is …

For each positive integer n, we temporarily say that a ring R is n-PF (^-pseudo-Frobenius) if
every faithful right i?-module generated by at most n elements is a generator for the category …

We investigate modules M having the injective property relative to nonsingular modules.
Such modules are called “N-injective modules”. It is shown that M is an N-injective R-module …

A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely
cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the …