关于C—环

主要讨论了C－环的结构以及它与其它环类之间的重要关系,从而较深刻地刻划这种环。     

关于Γ-除环

文中首先给出了定理２．２,由它可以行到文献「４」和「５」中关于Γ－域和除Γ－环的一些结果,其次,我们还指出了一个Γ－环是Γ－除环的几个条件。     

JC—环

本文定义了 JC一环,给出了 JC一环的结构.解决了 F.A.Szasz 在[1]中提出的公开问题94。     

对几类相关环的讨论

In this paper,the relations between a quasi-perfect ring,a coherent ring and a π-coherent ring are discussed.It is proved that a quasi-perfect ring is Morita equivalent.After that a moer popular ting,i.e,FGFT-ring,is discussed,some interesting properties are obtained.     

Г-环的单位元与其算子环的单位元之间的关系

г—环的单位元是其算子环中的元素.本文探讨Г—的单位与其算子环的单位元之间的关系.举例表明存在Г—环(Г_N—环)M,它的左、右算子环均有单位元,而M既无左单位元,又无右单位元.那么在什么条件下,Г—环(Г_N—环)的左、右算子环具有单位元时,其本身必定具有左、右单位元呢?对Г—环和Г_N—环分别探讨了此问题,并给出了了解答此问题的充要条件.     

FP—内射环和IF环的几个特征

本文给出了FP—内射环和IF环的如下几个特征:(l)R为右FP—内射环当且仅当任意左R—模正合列Kⁿ→Kⁿ→N→0 N为无挠模,当且仅当任一n阶矩阵环为右P—内射环;(2)R为左IF环当且仅当任一有限生成左R—模均可嵌入平坦模;(3)R为IF环当且仅当R为伪凝聚的上平坦环。     

正则环和GP-内射环

A ring R is called left Gp-injective if for any a∈R, there exists a positive integer n such that any left R-homomorphism of Raⁿ into R extends to one of R into R. In this paper, we prove that the centre of semiprime (left nonsingular) left GP- injective ring is regular ring, and improve some propositions in [3].     

关于NF-环的构造

研究了无限的ＮＦ－环及有限的ＮＦ－环，并且给出了有限ＮＦ－环的构造．     

PM环的扩张

A ring is called PM-ring if every primitive ideal is a intersection of its some maximal ideals.In this paper,the property of PM-ring is discussed and the necessary and sufficient condition are given for the polynomial,centralizing,strongly normal extensions of PM-ring to be PM-rings.We also get some applications of the extension of PM-ring in group ring.