An R-module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with
M= A 1⊕ A 2 and f: A 1→ A 2 is an R-homomorphism with ker f⊆⊕ A 1, we have I mf⊆⊕ A …

We introduce and study relative Rickart objects and dual relative Rickart objects in abelian
categories. We show how our theory may be employed in order to study relative regular …

ABSTRACT A right R-module M is called a U-module if, whenever A and B are submodules
of M with A≅ B and A∩ B= 0, there exist two summands K and L of M such that A⊆ ess K …

The present paper, is an extension and development of a serious of research papers
dealing with the semi-hollow lifting. Initially we proved semi hollow-lifting modules, by …

Open Access proceedings Journal of Physics: Conference series Page 1 Journal of Physics:
Conference Series PAPER • OPEN ACCESS Weakly Coretractable Modules To cite this …

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart
objects in abelian categories. Several types of abelian categories are characterized in terms …

A new generalizations of retractable modules relative to a submodule are introduced where
a module Script M is called retractable module relative to a submodule N of M if for all non …

We show how the theory of (dual) strongly relative Rickart objects may be employed in order
to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian …

In this paper, we introduce two new notions related with coretrectable modules which are
called essentially coretrectable and weakly essentially coretrectable modules. Some basic …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …