As a common generalization of Rickart ∗-rings and generalized Baer ∗-rings, we say that a
ring R with an involution ∗ is a generalized Rickart ∗-ring if for all x∈R the right annihilator …

We say that a-ring is a generalized Baer-ring if, for each nonempty subset of, the right
annihilator is generated as a right ideal by a projection for some positive integer depending …

Let R be a ring with identity. In this paper we introduce a strongly Rickart ring as a stronger
concept of a Rickart ring. A ring R is said to be strongly Rickart ring if the right annihilators of …

We introduce the notions of purely Baer and purely Rickart modules. We provide several
characterizations and investigate properties of each of these concepts. We provide new …

In this paper, we investigate rings in which the prime radical is an annihilator and present a
characterization of Artinian rings satisfying this property. We also study rings in which the …

A reduced Rickart ring is considered as a reduced ring R with an additional operation which
associates to every element a∈ R the single idempotent e such that the ideal eR is the right …

A ring R is called generalized right Baer if for any non-empty subset S of R, the right
annihilator rR (Sn) is generated by an idempotent for some positive integer n. Generalized …

In this paper we will define an ideal (NE (R)) which provides a link between the set of
nilpotents and the set of idempotents of a ring R. In the first section various properties of (NE …

This paper concerns two conditions, called right pp and generalized right pp, which are
generalizations of Baer rings and von Neumann regular rings. We study the subrings and …

We call a ring $ R $ generalized right $\pi $-Baer, if for any projection invariant left ideal $ Y
$ of $ R $, the right annihilator of $ Y^ n $ is generated, as a right ideal, by an idempotent, for …