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 …

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-weakly Hopfian modules which is a new
generalization of Hopfian modules. It is shown that over a ring R, every quasi-projective …

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 …

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 …

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 …

An R-module M is called t-weakly co-hopfian if any monomorphic endomorphism of M is t-
essential, which is discussed in [3]; still its property much familiar with weakly co-hopfian …

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} …

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 a proper generalization of that of Hopfian modules, called Jacobson …