A left module M over a ring R is cofaithful in case there is an embedding of R into a finite
product of copies of M. Our main result states that a semiprime ring R is left Goldie, that is …

In this paper, a new general theory of inject ivIiyroF" left R-modules is introduced. The
existence and unicity of the infective envelope of every module is established for a large …

Throughout this paper, R stands for an associative ring with unity and P-mod denotes the
category of all unitary left P-modules. A submodule A of В is small in В if A+ К= В implies К …

Abstract Recently, the (ρ, σ)-injectivity of modules with respect to a couple of preradicals has
boen investigaled. In the general case, the study of all the (ρ, σ)-injectivities reduces to that …

Generalized monoform and quasi injective modules Page 1 Pacific Journal of Mathematics
GENERALIZED MONOFORM AND QUASI INJECTIVE MODULES JOHN DAUNS Vol. 66, No …

It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence
between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion …

On L -Injective Modules arXiv:1501.02491v2 [math.RA] 11 Sep 2017 Page 1 On L -Injective
Modules Akeel Ramadan Mehdi Department of Mathematics College of Education Al-Qadisiyah …

This paper can be viewed as a continuation of our investigations [9] and is devoted to some
dual questions. Here we shall introduce a general type (in a certain sense) of the …

Let $\mathcal {M}=\{(M, N, f, Q)\mid M, N, Q\in R\text {-Mod},\, N\leq M,\, f\in\text {Hom} _
{R}(N, Q)\} $ and let $\mathcal {L} $ be a nonempty subclass of $\mathcal {M}. $ Jirásko …

In this paper, we show that injectivity with respect to the class $\mathcal {D} $ of dense
monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary …