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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 62, Pages 3949-3956
http://dx.doi.org/10.1155/S0161171203211339

On clean ideals

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

Received 21 November 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.