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 …

Throughout this paper R denotes an associative ring with unity. Recall from [Ka2) that R is a
Baer ring if the right annihilator of every nonempty subset of R is generated, as a right ideal …

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 …

The theory of Baer*-rings was set down in definitive form by Irving Kaplansky (its creator) in
1968, but the subject refuses to stop evolving; these notes are an attempt to record the …

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 …

Introduction. Let K be the ring of all n by n matrices over a division ring R. Then each left
(right) ideal of K is a principal left (right) ideal generated by an idempotent element. We may …

If R is a (right) self-injective regular ring then every closed right ideal is a direct summand.
Hence every annihilator right ideal is generated by an idempotent element; ie R is a Baer …

Extending the notion of a reduced ring, we call a right module M over a ring R a reduced
module if, for any m Є M and a€ R, ma= 0 implies mR Ma= 0. Various results of reduced …

We clarify and algebraicize the construction of the'regular rings' of finite Baer $^\ast $ rings.
We first determine necessary and sufficient conditions of a finite Baer $^\ast $ ring so that its …