We characterize a ring over which every left module of finite length has an injective hull of
finite length. Using this, we show that finite normalizing extensions of such a ring also have …

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 …

A module M is called N-almost-invariant for a module N if, for any homomorphism α: F→ E,
either α (N)⊆ M, or there exist nonzero direct summands F′ of F and E′ of E such that α …

Pure projective, pure injective and FP-injective modules over trivial ring extensions Page 1
Accepted manuscript to appear in IJAC Accepted Manuscript International Journal of Algebra and …

In this paper, we study the behavior of endomorphism rings of indecomposable (uniform)
quasi-injective modules. A very natural question here is, for a morphism f: A→ B, with A, B …

A ring extension is a ring homomorphism preserving identities. In this article, we establish
the relationship among relatively flat modules, relatively projective modules and relatively …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …