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 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 …

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 …

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 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 …

A ring R is called “quasi-Baer” if the right annihilator of every right ideal is generated, as a
right ideal, by an idempotent. It can be seen that a quasi-Baer ring cannot be a right …

The consistent way of investigating rings with involution, briefly*-rings, is to study them in the
category of*-rings with morphisms preserving also involution. In this paper we continue the …

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 …