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 …

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 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 …

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

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 …

Full article: Notes on Generalized Hopfian and Weakly Co-Hopfian Modules Skip to Main Content
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We carry out an extensive study of modules MR with the property that M/f (M) is singular for
all injective endomorphisms f of M. Such modules called “quasi co-Hopfian”, generalize co …

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 …