# UNIT-REGULARITY AND STABLE RANGE ONE

• Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
• Received : 2009.01.21
• Published : 2010.05.31
• 79 9

#### 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

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