Unit-regularity and stable range one
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 653-661
https://doi.org/10.4134/BKMS.2010.47.3.653
Published online May 1, 2010
Huanyin Chen
Hangzhou Normal University
Abstract : 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
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