It is well known that if R is a ring such that each right R-module Ž. embeds in a free module,
then R is a quasi-Frobenius QF ring. However, if the embedding is restricted to finitely …

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For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

According to Bourbaki [1, pp. 62–63, Exercise 11], a left (resp. right) A-module M is said to
be pseudo-coherent if every finitely generated submodule of M is finitely presented, and is …

Introduction. Injective modules, specially self-injective rings, occupy a prominent position in
ringtheory and have drawn the attention of many authors since several years (cf. for example …

Abstract Let (R,\frakm) be a commutative Noetherian complete local ring and let I be a
proper ideal of R such that the category of all I-cofinite R-modules is an Abelian subcategory …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …

We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

A module N∈ σ [M] is called cohereditary in σ [M] if every factor module of N is injective in σ
[M]. This paper explores the properties and the structure of some classes of cohereditary …