IF环和拟ZIF环

本文定义了拟ＺＩＦ环．研究了ＩＦ环与拟ＺＩＦ环的结构．进一步地，讨论了ＩＦ环与拟ＺＩＦ环的关系，并用拟ＺＩＦ环刻划了ＩＦ环．     

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.     

关于内射模的P-平坦性

通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件．     

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.     

相对遗传环

本文给出了左相对遗传环的概念及刻划.讨论了左相对遗传环与左遗传环,左半遗传环的关系,并给出了左遗传环的几个新的刻划.最后,证明了左相对遗传环(相对于左模范畴的生成元)的左理想的自同态环是左半遗传的;左相对遗传环(相对于左模范畴的内射生成元)上的有限生成相对投射模的自同态环是左半遗传的等结果.     

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.     

具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.     

The Rings Characterized by Minimal Left Ideals

We study these rings with every minimal left ideal being a projective, direct summand and a p-injective module, respectively. Some characterizations of these rings are given, and the relations among them are obtained. With these rings, we characterize seinisiinple rings. Finally, we introduce MC2 rings, and give some characterizations of MC2 rings.     

On Weakly Finite Conductor Rings

Abstract

We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results provide examples of a weakly finite conductor rings that are not finite conductor rings (and so not coherent rings). The last section show that the class of weakly finite conductor rings and the class of 2-coherent rings are not comparable.     

广义半交换环的幂零结构

研究了广义半交换环的幂零结构,定义了一类新的环类,即幂零$\alpha$-半交换环.说明了$\alpha$-半交换环与半交换环, $\alpha$-半交换环和$\alpha$-刚性环等环密切相关,通过构造反例说明了幂零$\alpha$-半交换环未必是$\alpha$-半交换环.研究了幂零$\alpha$-半交换环的各种性质,推广和统一了与环的半交换性质有关的若干结论.     

CODIMENSION AND REGULARITY OVER COHERENT SEMILOCAL RINGS

In this paper, the results on codimension and regularity over noetherian local rings and coherent local rings are extended to coherent semilocal rings and some useful examples of coherent semilocal rings are constructured.     

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.     

一类广义遗传环

称环R为左亚遗传环，如果内射左R－模的商模是FG－内射的，给出了左亚遗传环的一些刻划，给出了左亚遗传环的半单环的条件，并研究了左亚遗传环的一些性质。     

Endoprimitive rings

A class of endoprimitive rings is defined which contains all strongly prime rings and all weakly primitive rings. These rings are characterized in several ways and various facts about strongly prime and weakly primitive rings are generalized. An analog of the Jacobson radical is defined which is shown to be a normal radical lying between the Jacobson and Levitzki radicals.     

关于UR-环

A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.     

Rings in which elements are uniquely the sum of an idempotent and a unit that commute

A ring is called uniquely clean if every element is uniquely the sum of an idempotent and a unit. The rings described by the title include uniquely clean rings, and they arise as triangular matrix rings over commutative uniquely clean rings. Various basic properties of these rings are proved and many examples are given.     

p-内射性与Artin半单环

P-内射性在环论研究中有独特的作用,并且越来越被人们所重视.本文的目的是利用p-内射性来刻化Artin半单环,我们得到如下主要结果:(1)环R是Artin半单的当且仅当R是p-内射的,R的左奇异理想是闭右理想,且R满足特殊左零化子升链条件;(2)环R是Artin半单的当且仅当R的每个极大本质左理想是左零化子,并且任意奇异单左R-模是p-内射的;(3)素环R是Artin单的当且仅当R的右基层S≠0是左p-内射的,并且R满足特殊左零化子升链条件.这些结果不仅加深了对Artin半单环的认识,而且建立了半单环与某     

The topological jacobson radical of rings. II

In this paper, topologically primitive rings and rings possessing a faithful topologically irreducible module and bounded by this module are considered for the investigation of properties of their topological Jacobson radical. We investigate the topological Jacobson radical in some classes of topological rings such as left topologically Artinian rings, topological rings possessing a basis of neighborhoods of zero consisting of ideals, compact rings, and bounded strictly linearly compact 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.     

On the integral cohomology of a sylow subgroup of the symmetric group

Projectivity classes, which dualize injectivity classes (cf.[ll]), are introduced and some examples are given. Characterizations of hereditary rings, semisimple rings, Noetherian rings, (semi-)perfect rings, quasi-perfect rings, semiregular rings, semiregular modules and F- semiperfect modules using projectivity classes are given. Finally, for a projectivity class P, P-projective covers are defined and similar results with “quasi-projective cover” substituted by “T-projective cover” will still hold. Our results unify and generalize several well known results by Golan, Huynh and Smith, Rangaswamy and Vanaja, Tiwary and Pandeya, and Xue.