We say a ring with unity is right principally quasi-Baer (or simply, right pq-Baer) if the right
annihilator of a principal right ideal is generated (as a right ideal) by an idempotent. This …

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 …

A module M is called (strongly) F I-extending if every fully invariant submodule of M is
essential in a (fully invariant) direct summand of M. A ring R with unity is called quasi-Baer if …

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 …

A GENERALIZATION OF PP-RINGS AND pq-BAER RINGS Page 1 Glasgow Math. J. 48 (2006)
217–229. C 2006 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089506003016. Printed …

In this paper we carry out a systematic study of various ring theoretic properties of formal
triangular matrix rings. Some definitive results are obtained on these rings concerning …

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 …

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 …

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 …

Mason introduced the reflexive property for ideals, and then this concept was generalized by
Kim and Baik, defining idempotent reflexive right ideals and rings. In this article, we …