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 …

The class of biregular rings has repeatedly received attention as a test class for methods
applicable to rings without chain conditions. A ring is called biregular if every principal ideal …

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 …

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 …

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 the first section of this paper we extend the construction of the regular ring C, which was
defined in the work of SK Berberian [1],[2, Chapter 8]. The follow-ing theorem, the central …

We give a complete characterization of a certain class of quasi-Baer rings which have a
sheaf representation (by a “sheaf representation” of a ring the authors mean a sheaf …

A basic problem in ring theory is to investigate when a ring can be represented as the full
ring of endomorphisms of a suitable module. This problem in its full generality is quite …

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 …

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 …