Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

Rickart property for modules has been studied recently. In this article, we introduce and
study the notion of dual Rickart modules. A number of characterizations of dual Rickart …

The notion of Rickart modules was defined recently. It has been shown that a direct sum of
Rickart modules is not a Rickart module, in general. In this paper we investigate the …

Abelian groups whose endomorphism rings are von Neumann regular have been
extensively investigated in the literature. In this paper, we study modules whose …

Let⪯ be a preorder on a monoid H with identity 1 H and s be an integer≥ 2. The⪯-height of
an element x∈ H is the supremum of the integers k≥ 1 for which there is a (strictly)⪯ …

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 …

A ring is clean (almost clean) if each of its elements is the sum of a unit (regular element)
and an idempotent. A module is clean (almost clean) if its endomorphism ring is clean …

Let N be a submodule of a right R-module MR, and H= End (MR). Then N is said to be
projection invariant in M, denoted by N⊴ p M, if e N⊆ N for all e= e 2∈ H. We call MR π …

The purpose of this paper is to introduce the concept of strongly extending modules which
are particular subclass of the class of extending modules, and study some basic properties …

We study the transfer of (dual) relative Rickart properties via functors between abelian
categories, and we deduce the transfer of (dual) relative Baer property. We also give …