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1.
von-Neumann正则环与左SF-环   总被引:6,自引:0,他引:6  
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.  相似文献   

2.
研究了每一个极大左理想是弱右理想的环的性质.得到了左SF-环和强正则环的一些新的刻画,推广了一些已知的结论.  相似文献   

3.
研究了每一个极大左理想是弱右理想的环的性质.得到了SF-环和强正则环的一些新的刻画,推广了一些已知的结论.  相似文献   

4.
设环S是环R的优越扩张.本文证明了如一环是右IF-环;则另一环亦是,同时还得出了一个S是SF-环是正则的充要条件.  相似文献   

5.
N-环Von-Neumann正则性   总被引:10,自引:0,他引:10  
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.  相似文献   

6.
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:  相似文献   

7.
正则WB-环   总被引:1,自引:0,他引:1  
陈焕艮 《数学学报》2006,49(6):1311-132
引进了WB-环,研究了正则环为WB-环的等价刻画.如果A是正则环R上的有限生成投射右模而且M_n(R)都是WB-环(n∈N),若B,C是任何右R-模而且A⊕B≌A⊕C,证明了存在正交理想I,J,使得B/BI■~⊕C/CI且C/CJ■~⊕B/BJ.这也给出了QB-环上新的模比较性质.  相似文献   

8.
雷震 《大学数学》2008,24(1):29-32
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.  相似文献   

9.
GP-V'-环的von Neumann正则性   总被引:2,自引:0,他引:2  
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.  相似文献   

10.
每个本质左理想是幂等的MERT环   总被引:3,自引:0,他引:3  
环R称为MERT环,如果R的每个极大本质右理想是理想.本文证明了:每个本质左理想是幂等的半素MERT环一定是vonNeumann正则的.于是肯定地回答了Ming的一个公开问题.  相似文献   

11.
von Neumann Regular Rings and Right SF-rings   总被引:2,自引:0,他引:2  
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.  相似文献   

12.
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.  相似文献   

13.
Haiyan Zhou 《代数通讯》2013,41(12):3842-3850
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 article, we study the regularity of left SF-rings and we prove the following: 1) if R is a left SF-ring whose all complement left (right) ideals are W-ideals, then R is strongly regular; 2) if R is a left SF-ring whose all maximal essential right ideals are GW-ideals, then R is regular.  相似文献   

14.
研究了SF-环与P-内射环的关系,构造了SF-环成为P-内射环的一系列条件.证明了SF-环R只要满足其中之一:R的每个极大左理想是有限生成的;特殊右零化子的降链条件;对R的每个极大左理想M,l(M)在R中是本质的,那么R就是P-内射环.在此基础上,利用一定条件下SF-环的P-内射性,发展了SF-环的若干新结果,这些结果部分地拓展了有关文献中的结果.  相似文献   

15.
In an attempt to investigate the situation arising out of replacing additive regularity by additive complete regularity in our previous study on additively regular seminearrings, we introduce the notions of left (right) completely regular seminearrings and characterize left (right) completely regular seminearrings as bi-semilattices of left (resp., right) completely simple seminearrings. We also define left (right) Clifford seminearrings and show that they are precisely bi-semilattices of near-rings (resp., zero-symmetric near-rings).  相似文献   

16.
Nonlinear mappings in Banach spaces are considered. The covering property, metric regularity, and the existence of a continuous right inverse are considered for these mappings under various assumptions of smoothness. Several regularity conditions that guarantee the local covering property and the existence of a continuous right inverse are presented.  相似文献   

17.
For a unital ring, it is an open question whether flatness of simple modules implies all modules are flat and thus the ring is von Neumann regular. The question was raised by Ramamurthi over 40?years ago who called such rings SF-rings (i.e. simple modules are flat). In this note we show that an SF Steinberg algebra of an ample Hausdorff groupoid, graded by an ordered group, has an aperiodic unit space. For graph groupoids, this implies that the graphs are acyclic. Combining with the Abrams–Rangaswamy Theorem, it follows that SF Leavitt path algebras are regular, answering Ramamurthi’s question in positive for the class of Leavitt path algebras.  相似文献   

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