pi-Baer rings
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.17, no.2, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 17 Issue: 2
- Publication Date: 2018
- Doi Number: 10.1142/s0219498818500299
- Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Hacettepe University Affiliated: Yes
Abstract
We say a ring R is pi-Baer if the right annihilator of every projection invariant left ideal of R is generated by an idempotent element of R. In this paper, we study connections between the pi-Baer condition and related conditions such as the Baer, quasi-Baer and pi-extending conditions. The 2-by-2 generalized triangular and the n-by-n triangular pi-Baer matrix rings are characterized. Also, we prove that a n-by-n full matrix ring over a pi-Baer ring is a pi-Baer ring. In contrast to the Baer condition, it is shown that the pi-Baer condition transfers from a base ring to many of its polynomial extensions. Examples are provided to illustrate and delimit our results.