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 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 …

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 …

If R is a commutative semiprime ring with identity Kist [4],[5] has shown that R can be
embedded into a commutative Baer ring B (R), and has given some properties of this …

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 …

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 …

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 …

A ring R with unit element is a Baer ring if every left annihilator in R has the form Re, where e
is an idempotent element. KG Wolfson has proven [3, Corollary 15], that if R is a Priifer ring …

In this paper we give counterexamples to the following questions:(1) Are commutative
reduced rings Baer?,(2) Are commutative von Neumann regular rings Baer?,(3) Are reduced …

By a semiring we mean an algebra A=(A;+,-, 0) with two associative binary operations+,•
where+ is, moreover, commutative, and with a miliary operation 0 satisfying the distributive …