Π -Baer rings


Birkenmeier G. F. , Kara Y., TERCAN A.

Journal of Algebra and its Applications, vol.17, no.2, 2018 (SCI-Expanded) identifier identifier

  • 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
  • Keywords: Baer, quasi-Baer, projection invariant, pi-extending module, INTRINSIC EXTENSIONS, IDEALS, SETS
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2018 World Scientific Publishing Company.We say a ring R is π-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 π-Baer condition and related conditions such as the Baer, quasi-Baer and π-extending conditions. The 2-by-2 generalized triangular and the n-by-n triangular π-Baer matrix rings are characterized. Also, we prove that a n-by-n full matrix ring over a π-Baer ring is a π-Baer ring. In contrast to the Baer condition, it is shown that the π-Baer condition transfers from a base ring to many of its polynomial extensions. Examples are provided to illustrate and delimit our results.