Bulletin of the
Korean Mathematical Society BKMS

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