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 …

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 …

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\(\delta\) …

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 …

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 …

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 …

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 the notion of jacobson weakly Hopfian modules. It is shown that over a …

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 strongly Hopfian (respectively strongly co-Hopfian) if for every
endomorphism f of M the chain Kerf⊆ Kerf2⊆⋯(respectively Imf⊇ Imf2⊇⋯) stabilizes. The …