The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.
In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a ...In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a left GP-V'-ring containing an injective maximal left ideal and Soc(RR)(?)Soc(RR). Moreover, for an MELT ring R, it is shown that R is regular if and only if R is a left GP-injective left GP-V'-ring.展开更多
?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent sem...?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.展开更多
We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and...We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.展开更多
We introduce the zero-divisor graph for an abelian regular ring and show that if R,S are abelian regular, then (K0(R),[R])≌(K0(S),[S]) if and only if they have isomorphic reduced zero-divisor graphs. It is shown that...We introduce the zero-divisor graph for an abelian regular ring and show that if R,S are abelian regular, then (K0(R),[R])≌(K0(S),[S]) if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular, moreover, the zero-divisor graph of such a ring is studied.展开更多
Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relation...Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.展开更多
The upgrade of all kinds of algebraic structures has been emphasized with the development of fuzzy mathematics.The concept of hypergroup was raised first by Prof.LI Hong_xing in [1]and HX ring was done in [2].In thi...The upgrade of all kinds of algebraic structures has been emphasized with the development of fuzzy mathematics.The concept of hypergroup was raised first by Prof.LI Hong_xing in [1]and HX ring was done in [2].In this paper ,some properties of power ring and quasi_quotient ring are further studied based on paper [3～6].Especially,several theorems of homomorphism and isomorphism of regular power ring are established.展开更多
Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new...In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.展开更多
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 rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring...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 rings.It 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 R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.展开更多
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...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.展开更多
This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The st...This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The statement holds if the symmetric ring is replaced by reduced, 2-primal, left duo, right duo, abelian, NI, NCI, IFP, or Armendariz ring.展开更多
基金This work was supported in part by the NNSF (10071035) of China
文摘The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.
基金This work was partially support by the NNSF of China (No. 10171011) the NSF of JiangsuProvince in China (No. BK 2001001) the Younger Foundation (2003xqn04) of Anhui Normal University.
文摘In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a left GP-V'-ring containing an injective maximal left ideal and Soc(RR)(?)Soc(RR). Moreover, for an MELT ring R, it is shown that R is regular if and only if R is a left GP-injective left GP-V'-ring.
基金Supported by the National Natural Science Foundation of China（11161006, 11171142） Supported by the Natural Science Foundation of Guangxi Province（2011GXNSFA018144, 018139, 2010GXNSFB 013048, 0991102）+2 种基金 Supported by the Guangxi New Century 1000 Talents Project Supported by the Guangxi Graduate Student Education Innovation Project（2011106030701M06） Supported by the SRF of Guangxi Education Committee
文摘In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.
文摘?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.
基金supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)
文摘We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.
基金Partially supported by the NSF (10071035) of China.
文摘We introduce the zero-divisor graph for an abelian regular ring and show that if R,S are abelian regular, then (K0(R),[R])≌(K0(S),[S]) if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular, moreover, the zero-divisor graph of such a ring is studied.
基金Foundation item:This work is partially supported by the NNSF(10171011)of Chinathe NNSF(10571026)of Chinathe Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutes of MOE,P.R.C.
文摘Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.
文摘The upgrade of all kinds of algebraic structures has been emphasized with the development of fuzzy mathematics.The concept of hypergroup was raised first by Prof.LI Hong_xing in [1]and HX ring was done in [2].In this paper ,some properties of power ring and quasi_quotient ring are further studied based on paper [3～6].Especially,several theorems of homomorphism and isomorphism of regular power ring are established.
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
文摘In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.
基金supported by the grant of National Natural Science Foundation of China(10971024)the Nanjing University of Posts and Telecommunications(NY209022)
文摘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 rings.It 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 R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.
基金The Scientific Research Foundation(12B101)of Hunan Provincial Education Department
文摘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.
文摘This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The statement holds if the symmetric ring is replaced by reduced, 2-primal, left duo, right duo, abelian, NI, NCI, IFP, or Armendariz ring.
