关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.     

强正则环的刻划

强正则环的刻划胡卫群（安徽省滁州师范专科学校）Ａｕｓｌａｎｄｅｒ在［３］中证明了：环Ａ是ＶｏｎＮｅｕｍａｎｎ正则的对于Ａ的任意左理想Ｌ与Ａ的任意右理想Ｒ，，总有ＲｎＬ＝ＲＬ．Ｒ．ＹｕｅＣｈｉＭｉｎｇ在［２］中推广了Ａｕｓｌａｎｄｅｒ［３］的结果，证明...     

von-Neumann正则环与左SF-环

环R称为左SF-环,如果每个单左R-模是平坦的.众所周知,Von-Neumann正则环是SF-环,但SF-环是否是正则环至今仍是公开问题,本文主要研究左SF-环是正则环的条件,证明了:如果R是左SF-环且R的每个极大左(右)理想是广义弱理想,那么R是强正则环.并且推广了Rege[3]中的相应结果.     

关于半交换环与强正则环

本文得到了环Ｒ是强正则环的若干充分必要条件，证明了下面条件是等价的：（１）Ｒ是强正则的；（２）Ｒ是半交换正则的；（３）Ｒ是半交换的左ＳＦ－环；（４）Ｒ是半交换的ＥＬＴ环，且使得每个单左Ｒ－模是Ｐ－内射的或者平坦的；（５）Ｒ是半交换右非奇异的左ＳＦ－环；（６）Ｒ是半素的半交换左（或右）Ｐ－内射环．     

关于GP-V’-环的强正则性

本文研究了GP-V,GP-V’-环的Von Neumann正则性问题.利用GW-理想和拟ZI-环的性质及方法,得到了GP-V,GP-V’-环是强正则环的一些条件,推广了文献[4]和文献[6]的相关结果.     

GP-V'-环的von Neumann正则性

本文研究了GP-V'-环的von Neumann正则性问题.利用GW-理想和W-理想的性质及方法,得到了 GP-V'-环是(强)正则环的一些条件,推广了文献[3,6]中的相关结果.     

直觉模糊强正则子环及其同态

给出了直觉模糊强正则子环的定义,讨论了它的一些基本性质,得到了两个直觉模糊强正则子环的交仍是直觉模糊强正则子环,并利用直觉模糊集的截集给出了直觉模糊强正则子环的等价刻画。最后研究了直觉模糊强正则子环的同态像与原像的性质。     

几乎强正则环及其扩张

在强正则环的基础上引入几乎强正则环的概念,它们是介于局部环和VNL环之间的一类环.给出几乎强正则环的若干例子,讨论它们的扩张.     

Characterizations of Strongly Regular Rings

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＳｔｒｏｎｇｌｙＲｅｇｕｌａｒＲｉｎｇｓＺｈａｎｇＪｕｌｅ（章聚乐）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈｕ２４１０００）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...     

关于单位正则环

本文得到了单位正则环的一个新特征,证明了:正则环R为单位正则环当且仅当存在理想I使得(1)R/I为单位正则环;(2)对任何a∈R,存在理想J满足JI=0和a=aua,其中u模J左可逆.作为应用,利用零化子理想刻画了单位正则环.     

On Real Closed Regular Rings

The aim of this paper is to investigate some properties of real closed regular rings, in particular, the role played by real place in a real closed regular ring.2000 Mathematics Subject Classification: 13J25This work was supported by NSF of Jiangxi Province, China.     

On Von Neumann Regular Rings of Skew Generalized Power Series

In this paper we introduce a construction called the skew generalized power series ring R[[S, ω]] with coefficients in a ring R and exponents in a strictly ordered monoid S which extends Ribenboim's construction of generalized power series rings. In the case when S is totally ordered or commutative aperiodic, and ω(s) is constant on idempotents for some s ∈ S?{1}, we give sufficient and necessary conditions on R and S such that the ring R[[S, ω]] is von Neumann regular, and we show that the von Neumann regularity of the ring R[[S, ω]] is equivalent to its semisimplicity. We also give a characterization of the strong regularity of the ring R[[S, ω]].     

Abel正则球与完全正则半群

本文分别讨论了关于结合环和半群的二个定理，并且由结合环的这二个定理推出了如下准则：结合环Ｒ是Ａｂｅｌ正则的，当且仅当Ｒ的每个拟理想是正则环．     

On Strongly Regular Rings

In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.     

von Neumann Regular Rings and Right SF-rings

A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings and prove that if R is a right SF-ring whose all maximal (essential) right ideals are GW-ideals, then R is regular.     

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.