Bull. Korean Math. Soc. 2005; 42(1): 45-51
Printed March 1, 2005
Copyright © The Korean Mathematical Society.
Huanyin Chen and Miaosen Chen
Zhejiang Normal University, Zhejiang Normal University
In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a $qb$-ideal. It is shown that an exchange ideal $I$ of a ring $R$ is a $qb$-ideal if and only if whenever $a{\overline \sim}b$ via $I$, there exists $u\in I_q^{-1}$ such that $a=ubu_q^{-1}$ and $b=u_q^{-1}au$. This gives a generalization of the corresponding result of exchange $QB$-rings.
Keywords: exchange ideal, $qb$-ideal
MSC numbers: 16E50, 16U99
2005; 42(2): 295-305
2009; 46(3): 489-498
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