International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 62, Pages 3949-3956
doi:10.1155/S0161171203211339
On clean ideals
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
Received 21 November 2002
Copyright © 2003 Huanyin Chen and Miaosen Chen. 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.