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International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 62, Pages 3949-3956
doi:10.1155/S0161171203211339

On clean ideals

Huanyin Chen and Miaosen Chen

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

Received 21 November 2002

Abstract

We introduce the notion of clean ideal, which is a natural generalization of clean rings. It is shown that every matrix ideal over a clean ideal of a ring is clean. Also we prove that every ideal having stable range one of a regular ring is clean. These generalize the corresponding results for clean rings.