On exchange ${\text\bf qb}$-ideals
Bull. Korean Math. Soc. 2005 Vol. 42, No. 1, 45-51
Published online March 1, 2005
Huanyin Chen and Miaosen Chen
Zhejiang Normal University, Zhejiang Normal University
Abstract : 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
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