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 …

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 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 a concept of a dual F-Baer module M where F is the fully invariant
submodule of M, by this means we deal with generating dual Baer modules. We investigate …

The submodule in its injective hull is small} is investigated by Talebi und Vanaja for every R-
module M. We solve the three problems which were put forth in that work by replacing the …

Let R be an arbitrary ring with identity, M a right R-module and F a fully invariant submodule
of M. The notion of an F-inverse split module M has been defined and studied by the present …

Over an arbitrary ring, a module M is said to be Z∗ Z^ ∗-semilocal if every submodule U of M
has a Z∗ Z^ ∗-supplement V in M, ie, M= U+ V and U∩ V⊆ Z∗ V, U ∩\kern0. 5em V ⊆ Z^ ∗ …

Let M be a right R-module. Define Z (N)(8 M (N)) to be the set of elements ne N for any R-
module N in a [M] such that nR is an M-small (respectively 8-M-small) modüle. In this note it …

This paper aims to introduce the concepts of 𝑒∗-closed, 𝑒∗-coclosed, and 𝑒∗-extending
modules as generalizations of the closed, coclossed, and extending modules, respectively …