The concepts Rickart rings and Baer rings have their roots in the theory of linear operators in
Hilbert space. The concept of Baer rings was introduced by I. Kaplansky in 1955 and the …

We introduce the notions of Baer and quasi-Baer properties in a general module theoretic
setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) left ideal of …

Let R be an arbitrary ring with identity and M a right R-module with S= End R (M). Let F be a
fully invariant submodule of M and I− 1 (F) denotes the set {m∈ M: Im⊆ F} for any subset I of …

We introduce the notions of the Baer and the quasi-Baer properties in a general module
theoretic setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) …

A purely extending module is a generalization of an extending module. In this paper, we
study several properties of purely extending modules and introduce the notion of purely …

We introduce and study the notion of wd-Rickart modules (ie modules M such that for every
nonzero endomorphism ϕ of M, the image of ϕ contains a nonzero direct summand of M) …

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 …

Let R be an arbitrary ring with identity and M a right R-module with S= EndR (M). In this
paper, we introduce a class of modules that is a generalization of principally quasi-Baer …

Let R be a ring and let M be an R-module with S= End _R (M) S= End R (M). The module M
is called quasi-dual Baer if for every fully invariant submodule N of M,{ϕ ∈ S ∣ Im ϕ ⊆ N\} …

We consider Baer rings and Baer semisimple $ R $-modules which are generalizations of
semisimple modules. Several characterization theorems of Baer semisimple modules are …