J. Korean Math. Soc. 2008; 45(3): 741-756
Printed May 1, 2008
Copyright © The Korean Mathematical Society.
Huanyin Chen
Hunan Normal University
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.
Keywords: $SB$-ring, semilocal ring, exchange ring
MSC numbers: 16E50, 19U99, 15A33
2008; 45(2): 425-433
2010; 47(4): 819-830
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