In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely gene...In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.展开更多
This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
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
In this paper. we study the endomorphism rings of regular modules.We give sufficient conditions on a regular projective module P such that End_R(P) has stable range one.
文摘In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.
文摘This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
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.
基金The author is supported by the NNSF of China (No. 19601009)
文摘In this paper. we study the endomorphism rings of regular modules.We give sufficient conditions on a regular projective module P such that End_R(P) has stable range one.
