ON SB-RINGS
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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
Abstract
In this paper, we introduce a new class of rings, SB-rings. Weestablish various properties of this concept. These shows that, in severalrespects, SB-rings behave like rings satisfying unit 1-stable range. Wewill give necessary and sufficient conditions under which a semilocal ringis a SB-ring. Furthermore, we extend these results to exchange ringswith all primitive factors artinian. For such rings, we observe that theconcept of the SB-ring coincides with Goodearl–Menal condition. Thesealso generalize the results of Huh et al., Yu and the author on ringsgenerated by their units
참고문헌 (13)
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