On Ideals of Regular Rings |
| |
| Authors: | Huan Yin Chen Fu An Li |
| |
| Institution: | (1) Department of Mathematics, Hunan Normal University, Changsha 410006, P.R. China E-mail: chyzxl@sparc2.hunnu.edu.cn, CN;(2) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China E-mail: fal@math08.math.ac.cn, CN |
| |
| Abstract: | In this paper, we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the comparability.
In addition it is shown that, if I is a minimal two-sided ideal of a regular ring R, then I satisfies the comparability if and only if I is separative. Furthermore, we prove that, for ideals with stable range one, Roth's problem has an affirmative solution.
These extend the corresponding results on unit-regularity and one-sided unit-regularity.
Received February 20, 2001, Accepted July 20, 2001 |
| |
| Keywords: | Regular ring Comparability Stable range one Roth's problem |
| 本文献已被 SpringerLink 等数据库收录！ |
|
