The notion of Baer modules was defined recently. Since a direct sum of Baer modules is not
a Baer module in general, an open question is to find necessary and sufficient conditions for …

We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-
nonsingular modules properly contains the classes of nonsingular modules and of polyform …

Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce
the concept small monoform module as a generalization of monoform module. A module M …

In this article, we study the notion of closed Rickart modules. A right R-module M is said to
be closed Rickart if, for each, is a closed submodule of M. Closed Rickart modules is a …

In this paper we introduce and study the concept of strongly Rickart modules and strongly
CS-Rickart modules as a stronger than of Rickart modules [8] and CS-Rickart modules [3] …

A module MR is called principally quasi-Baer (or simply pq-Baer) if the annihilator of every
cyclic submodule of MR is generated by an idempotent, as a right ideal. Let α be an …

The study of the endomorphism rings of modules and connections between a module and its
endomorphism ring have long been of interest. Of particular interest has been a quest of …

It is of obvious interest to know whether an algebraic property of modules is preserved by
direct sums of such modules. In this paper we provide a survey of this question for various …

Let 𝑅 be a ring with identity. Recall that a submodule 𝑁 of a left 𝑅-module 𝑀 is called
strongly essential if for any nonzero subset 𝑋 of 𝑀, there is 𝑟∈ 𝑅 such that (0≠) 𝑟𝑋⊆ 𝑁 …