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New York Journal of Mathematics 9 (2003), 295-302.

On unit-regular ideals

Huanyin Chen and Miaosen Chen

Published: November 19, 2003
Keywords: unit-regular ideal, diagonal reduction, pseudo-similarity
Subject: 16E50, 16U99

Abstract:

In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity.

Author information:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, People's Republic of China
chyzxl@sparc2.hunnu.edu.cn
miaosen@mail.jhptt.zj.cn