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 …

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 …

Introduction. Kaplansky [6] introduced the Baer rings as rings in which every left (right)
annihilator ideal is generated by an idempotent. The motivation comes from the observation …

We say that a*-ring R is a generalized quasi-Baer*-ring if for any ideal I of R, the right
annihilator of I n is generated, as a right ideal, by a projection, for some positive integer n …

Throughout this paper all rings are associative with identity and all modules are unital.
Recall from [20] that R is a Baer ring if the right annihilator of every nonempty subset of R is …

In this note we study commutative Baer rings, uniting the abstract algebraic approach with
the approach of [3] using minimal prime ideals. Some new characterisations of this class of …

0. Introduction. Throughout this paper R denotes an associative ring with unity. If an
involution* is defined on R, then R is called a*-ring. If X is a nonempty subset of R, then X is …

A commutative ring A is called a Baer ring if the annihilator of each element in A is the
principal ideal generated by an idempotent. It is shown that the following three conditions on …

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 …

A systematic exposition of Baer*-Rings, with emphasis on the ring-theoretic and lattice-
theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio …