Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a ring, and let $\Psi(R)$ be the ideal generated by the set $\{x\in R~|~ 1+sxt\in R$ is unit-regular for all $s,t\in R\}$. We show that $\Psi (R)$ has ``radical-like" property. It is proven that $\Psi(R)$ has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.

Keywords: unit-regularity, stable range one, diagonal reduction

MSC numbers: 16E50, 16U99