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 …

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 …

Necessary and sufficient conditions are obtained for extending the involution of a Baer $\ast
$-ring to its maximal ring of quotients. Berberian's construction of the regular ring of a Baer …

Full article: A NOTE ON PRINCIPALLY QUASI-BAER RINGS Skip to Main Content Taylor and
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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 a left AIP-ring if the left annihilator of any ideal of R is pure as a left ideal.
Equivalently, R is a left AIP-ring if R modulo the left annihilator of any ideal is flat. This class …

The theory of Baer*-rings was set down in definitive form by Irving Kaplansky (its creator) in
1968, but the subject refuses to stop evolving; these notes are an attempt to record the …

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 …

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 …

The notion of a direct summand of a ring containing the set of nilpotents in some “dense”
way has been considered by Y. Utumi, L. Jeremy, C. Faith, and GF Birkenmeier. Several …