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 …

In this paper, we introduce the notion of\(\delta\)-Hopfian modules. We give some properties
of these modules and provide a~ characterization of semisimple rings in terms of\(\delta\) …

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 …

In this paper we introduce the notion of μ μ-Hopfian modules which is a proper
generalization of that of Hopfian modules. We give some characterizations and properties of …

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 a proper generalization of that of Hopfian modules, called
$\gamma $-Hopfian modules. A right $ R $-module $ M $ is said to be $\gamma $-Hopfian, if …

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 …

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 …

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 study of modules by properties of their endomorphisms has long been of interest. In this
paper we introduce a proper generalization of that of Hopfian modules, called Jacobson …