UNIT-REGULARITY AND STABLE RANGE ONE

Chen, Huanyin

doi:10.4134/BKMS.2010.47.3.653

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UNIT-REGULARITY AND STABLE RANGE ONE

Journal title : Bulletin of the Korean Mathematical Society
Volume 47, Issue 3, 2010, pp.653-661
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2010.47.3.653

Title & Authors

UNIT-REGULARITY AND STABLE RANGE ONE
Chen, Huanyin;

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;

Language

English

Cited by

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