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 …

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 …

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 …

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 and study the concept of Jacobson monoform modules whichis a
proper generalization of that of monoform modules. We present a characterization of …

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 …

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 μ μ-Hopfian modules which is a proper
generalization of that of Hopfian modules. We give some characterizations and properties of …

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 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 …