In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient)
morphisms. Then we give a characterization of this new concept. We show that an …

We derive a necessary and sufficient condition that an isomorphism between the
endomorphism rings of modules be induced by a semi-linear isomorphism of the modules …

A ring $ R $ is said to have a left Morita duality with a ring $ S $ if there is an additive
contravariant equivalence between two categories of left $ R $-modules and right $ S …

An R-module M is called weakly Hopfian (respectively generalized co-Hopfian) if for every
small epimorphism (respectively essential monomorphism) f of M is isomorphism. If M is …

A module M is called an automorphism-invariant module if every isomorphism between two
essential submodules of M extends to an automorphism of M. This paper introduces the …

Let R be a ring and 𝑆 be a class of some finitely generated left R-modules. Then a left R-
module M is called 𝑆-projective if for every homomorphism f: S→ M, where S∈ 𝑆, there exist …

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 …

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

We first prove that if a monomorphism is a phantom envelope of a left R-module, then its
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …

A family C of finitely generated indecomposable modules is said to have right almost split
morphisms if there is a right almost split morphism f: N→ M in add C for each …