UNIT-REGULARITY AND STABLE RANGE ONE

Title & Authors
UNIT-REGULARITY AND STABLE RANGE ONE
Chen, Huanyin;

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