- ON SB-RINGS
- Chen, Huanyin ;
- Journal of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 741~756
- DOI : 10.4134/JKMS.2008.45.3.741

Abstract

In this paper, we introduce a new class of rings, SB-rings. We establish various properties of this concept. These shows that, in several respects, SB-rings behave like rings satisfying unit 1-stable range. We will give necessary and sufficient conditions under which a semilocal ring is a SB-ring. Furthermore, we extend these results to exchange rings with all primitive factors artinian. For such rings, we observe that the concept of the SB-ring coincides with Goodearl-Menal condition. These also generalize the results of Huh et al., Yu and the author on rings generated by their units.