Morphic环和G-morphic环的一些结果

讨论了morphic环,G-morphic环,PP环,GPP环,Bear环与正则环之间的关系.还证明了在约化环中,强正则环,正则环,π-正则环,G-π-正则环的等价性.     

环的弱正则性

本文给出了环的弱正则性的一个充要条件，还讨论了Ｍｕｎｎ环的弱正则性．最后对环的半格和及补半格和，给出了弱正则性的刻画．     

准正则环与正则环

每一个主左理想均由一个幂等元生成的环叫正则环。每一个左理想均由若干个幂等元生成的环叫准正则环。本文研究准正则环与正则环的一些性质，讨论准正则环成为正则环的一些条件，准正则环、正则环与Ｖ环之间的关系，准正则环成为Ａｂｅｌ正则环的条件。     

Abel正则环的k0及其模范畴的等价性

本文给出了Ａｂｅｌ正则环的ｋｏ结构并且利用Ｍｏｒｉｔａ Ｃｏｎｔｅｘｔ证明了Ａｂｅｌ正则环的模范畴的Ｍｏｒｉｔａ等价性。     

关于右SF-环的正则性(英文)

研究了每一个极大的右理想是拟理想的右SF-环的正则性,得到了右SF-环是正则环的一些新的刻画,推广了一些已知的结论.     

N-环Von-Neumann正则性

环R称为N-环,如果R的素根N(R)=｛r∈R｜存在自然数n使rⁿ=0}.本文不仅对N-环进行了刻划,而且还研究了N-环的VonNeumann正则性.特别证明了：对于N-环R,如下条件是等价的：(1)R是强正则环;(2)R是正则环;(3)R是左SP-环;(4)R是右SF-环;(5)R是MELT,左p-V-环;(6)R是MERT,右p-V-环.因此推广了文献[4]中几乎所有的重要结果,同时也改进或推广了其它某些有关正则环的有用结果.     

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.     

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.     

关于Von Neumann正则环的一个问题

设A是结合环,如果α∈αAα,(?)α∈A,则称A是Von Neumann正则环,以下简称正则环.环A的理想ι称为A的正则理想,如果ι作为环是正则环.结合环A的元素α叫做双正则元素,如果α在A中生成的主理想(α)有单位元.所有元都是双正则元的环叫做双正则环.如果环A的理想ι是双正则环,测称ι是A的双正则理想.我们知道,对任意结合环A,存在最大的正则理想(?)(A)和最大的双正则理想B(A).正则环全体之类(?)是Amitsur—Kurosh意义下的一个根环类,而且是一个遗传类.关于最大的双正则理想,Szasz在[1]的定理44.9中给出了如下结论:     

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.     

$GP$-$V^{''}$-环的非奇异性与正则性

In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results.     

A Regularity Criterion for Semigroup Rings

An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings.     

Some minimal rings related to 2-primal rings

In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS I were given in order to show that the ring class inclusions were strict. Many of the rings given in the examples were infinite. In this paper, where possible, examples of minimal finite rings of the various types are given. Along with the rings in the previous taxonomy, NI, abelian and reflexive rings are also included.     

弱$r$-Clean环

As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a∈R there exist an idempotent e and a regular element r such that a = r + e or a = r-e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean rings and weakly r-clean rings are equivalent for abelian rings.     

广义半π-正则环

In this paper, the concept of right generalized semi-w-regular rings is defined. We prove that these rings are non-trival generalizations of both right GP-injective rings and semi- π-regular rings. Some properties of these rings are studied and some results about generalized semiregular rings and GP-injective rings are extended.     

McCoy Rings Relative to a Monoid

For a monoid M, we introduce M-McCoy rings, which are a generalization of McCoy rings and M-Armendariz rings; and investigate their properties. We first show that all reversible rings are right M-McCoy, where M is a u.p.-monoid. We also show that all right duo rings are right M-McCoy, where M is a strictly totally ordered monoid. Then we show that semicommutative rings and 2-primal rings do have a property close to the M-McCoy condition. Moreover, it is shown that a finitely generated Abelian group G is torsion free if and only if there exists a ring R such that R is G-McCoy. Consequently, several known results on right McCoy rings are extended to a general setting.     

半正则环的推广

In this paper, the concept of generalized semiregular rings is extended to generalized weak semiregular rings. Some properties of these rings are studied and some results about semiregular rings and generalized semiregular rings are extended. We also give some equivalent characterizations ofI-weak semiregular rings.     

广义半$\pi$-正则环

In this paper, the concept of right generalized semi-π-regular rings is defined. We prove that these rings are non-trival generalizations of both right GP-injective rings and semi- π-regular rings. Some properties of these rings are studied and some results about generalized semiregular rings and GP-injective rings are extended.     

Some Regularity Criteria for Affine Semilocal Rings

The purpose of this article is to study an existence of p-bases and mainly to give some regularity criteria for semilocal rings essentially of finite type over fields.