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 …

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 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 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 …

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 …

1. Introduction. In [41 KAPLANSKY has used the term Baer ring to denote those rings in
which the left (right) annihilator of each subset is'a principal left (right) ideal generated by an …

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 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 …

Let MR be an arbitrary module. Then Mn is a JBaer module in case it satisfies Baer's
condition (the terminology of [2] will be used throughout), namely, in case for each [e HomR …