Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

In this paper we introduce-non-cosingular modules, dual Baer modules and-modules. We
prove that a module M is lifting and-non-cosingular if and only if it is a dual Baer and …

ABSTRACT PF Smith studied modules in which every submodule has a unique closure and
called them UC modules. In this paper we consider modules with the dual property viz …

Many observations about coalgebras were inspired by comparable situations for algebras.
Despite the prominent role of prime algebras, the theory of a corresponding notion for …

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 …

After pubertal, cohort of small antral follicles enters to gonadotrophin-sensitive development,
called recruited follicles. This study was aimed to identify candidate genes in follicular cyclic …

In this paper, the structure of e-local modules and classes of modules via essentially small
are investigated. We show that the following conditions are equivalent for a module M:(1) M …

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 be a finite direct sum of modules. We prove:(i) If Mi is radical Mj-projective for all j> i and
each Mi is H-supplemented, then M is H-supplemented.(ii) If all the Mi are relatively …

Lifting modules as a main concept in module theory have been studied and investigated
extensively in recent decades. The first author in [1] tried to consider and investigate this …