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 …

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

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 …

Baer rings are rings in which the left (right) annihilator of each subset is generated by an
idempotent [6]. Closely related to Baer rings are left PP-rings; these are rings in which each …

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 …

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 …

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 ring R with unity is called a (quasi-) Baer ring if the left annihilator of every (left ideal)
nonempty subset of R is generated (as a left ideal) by an idempotent. Armendariz has shown …

The Regular Ring of a Finite Baer *-Ring Page 1 Chapter 8 The Regular Ring of a Finite Baer
*-Ring The present chapter is based on 181. 5 46. Preliminaries At the outset we assume that …