On Ideals of Regular Rings  

作　　者：CHEN Huan Yin Department of Mathematics,Hunan Normal University.Changsha 410006.P.R.China E-mail:[e-mail] Fu An 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 

出　　处：《Acta Mathematica Sinica,English Series》2002年第2期347-356,共10页数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant;No.19801012);the Ministry of Education of China

摘　　要：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.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.

关 键 词：Regular ring Comparability Stable range one Rothis problem 

分 类 号：O153.3[理学—数学]