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
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.