The structures of Hopfian and co-Hopfian modules over commutative rings are studied. The
notation of semi Hopfian (resp. semi co-Hopfian) modules as a generalization of that of …

In this paper, we introduce the notion of µ-weakly Hopfian modules which is a new
generalization of Hopfian modules. It is shown that over a ring R, every quasi-projective …

Let R be a ring and M a left R‐module. M which satisfies DCC on essential submodules is
GCH, and M which satisfies ACC on small submodules is WH. If M [X] is GCH R [X]‐module …

Ar-module M is said to be Hopfian (respectively Co-Hopfian) in case any surjective
(respectively injective) R-homomorphism is automatically an isomorphism. In this paper we …

A module M is called semi co-Hopfian (resp. semi Hopfian) if any injective (resp. surjective)
endomorphism of M has a direct summand image (resp. kernel). We show that if M is semi …

Full article: Notes on Generalized Hopfian and Weakly Co-Hopfian Modules Skip to Main Content
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The concept of Hopfian modules has been extensively studied in the literature. In this paper,
we introduce and study the notion of δ-weakly Hopfian modules. The class of δ-weakly …

The main aim of this paper is the Hopficity of module classes, the study of modules (rings) by
properties of their endomorphisms is a classical research subject. In 1986, Hiremath\cite {Hi} …

Full article: Duality for Weakly Co-Hopfian and Generalized Hopfian Modules Skip to Main
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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 …