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...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.展开更多
基金supported by the National Natural Science Foundation of China (GrantNo.19801012)the Ministry of Education of China
文摘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.
