von Neumann正则环与右SF-环

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.     

关于周期环结构的几个定理

本文给出了有关周期环结构的一些结果,而使文献[1]中的所有定理都可以做为本文结果的直接结论。     

On π-regularity of General Rings

A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left （right） semicentral if for every x ∈ I,xe=exe （ex=exe）.And I is called semiabelian if every idempotent in I is left or right semicentral.It is proved that a semiabelian general ring I is π-regular if and only if the set N （I） of nilpotent elements in I is an ideal of I and I /N （I） is regular.It follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-regular.Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring.These generalize several known results on the relevant subject.Furthermore we give a characterization of a semiabelian GVNL-ring.     

Von Neumann正则环的几点注记

本文利用理想化子的概念定义了duo环的一个推广,称为MD环,并且研究了MD环的一些性质.特别地.我们证明了:如果R是MD环,且每一个奇异单左R-模是p-内射的,那么R是指数有界的von Ncumann正则环,因此,R.Yue chi ming提出的如下公开问题得到了肯定的回答:GLD左Γ-环是否为Von ncumann正则的?     

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:     

半素环上(右)广义自同构的扩张

In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.     

关于L内射覆盖

We use the class of L-injective modules to define L-injective covers, and provide the characterizations of L-injective covers by the properties of kernels of homomorphisms. We prove that the right L-noetherian right L-hereditary ring is just such that every right R-module has an L-injective cover which is monic. We also use kernels of homomorphisms to investigate L-simple L-injective covers and give some constructions of L-simple L-injective covers.