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On Ideals of regular rings

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Acta Mathematica Sinica,English Series 2002年第2期18卷 347-356页

作者： CHEN Huan Yin Department of Mathematics,Hunan Normal University.Changsha 410006.P.R.China E-mail:chyzxl@sparc2.hunnu.edu.cnLI Fu An Institute of Mathematics.Academy of Mathematics and System Sciences Chinese Academy of Sciences,Beijing 100080,P.R,China E-mail:fal@math08,*** Department of Mathematics Hunan Normal University Changsha P.R. China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing P.R. China

in this paper,we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the *** addition,it is shown *** I is a minimal two-sided ideal of a regular ring R,then I satisfies the Comparability if and only if I is ***,we prove *** ideals with stable range ***'s problem has an affirmative *** extend the corresponding results on unit-regularity and one-sided unit-regularity.

关键词： regular ring Comparability Stable range one Rothis problem

NOETHERIAN GT-regular ringS ARE regular

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 463-468页

作者： LI HUISHI(Department of Mathematics, Shaanxi Normal Univisity Xi’an 710062, China.) 陕西师范大学数学系陕西西安 710062

It is proved that for a left Nootherian z-graded ring A, if every finitely generated gradedA-module has finite projective dimension (i.e., A is gr-regular) then every finitely generatedA-module has finite projective dimension (i.e., A is regular). Some applications of this resultto filtered rings and some classical cases are also given.

关键词： Graded ring regular ring Projective dimension.

Some Characterizations of GVNL rings

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南京邮电大学学报（自然科学版） 2011年第5期31卷 121-123页

作者： YING Zhi-ling College of Science Nanjing University of Posts and Telecommunications Nanjing 210046 China

A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular *** is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring for every idempotent e of *** prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is *** formal power series ring R[x] is GVNL if and only if R is a local ring.

关键词： GVNL ring VNL ring regular ring local ring

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On Weakly P.P. rings

Communications in Mathematical Research 2015年第4期31卷 362-372页

作者： Xiang Yue-ming Ouyang Lun-qun Wang Shu-gui Du Xian-kun Department of Mathematics and Applied Mathematics Huaihua University Department of Mathematics Hunan University of Science and Technology

We introduce, in this paper, the right weakly p.p. rings as the generaliza- tion of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.

关键词： weakly p.p. ring GP-injective module regular ring

The Relative Properties of Graded ring R and Smash Product R # G

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Chinese Quarterly Journal of Mathematics 1995年第3期10卷 32-36页

作者：魏俊潮李立斌 Yangzhou Institute

Led G he a group, R be a G-graded ring, R,this paper deals with some relative properties of R and smash product R # G .We give out R is graded regular ring,graded right SF-ring, graded right V-ring, graded QF-ring if... 详细信息

关键词： graded ring smash product regular ring