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1.
模的弱消去问题与qu-正则环   总被引:1,自引:0,他引:1  
本文考虑模的弱消去问题与正则环的Stablerange条件,引进了qu-正则环的概念,并用它刻划了一类满足弱消去条件的模,刻划了qu-正则环,指出一切满足比较公理的正则环均为qu-正则环.文中还考虑这些结果的应用.例如,刻划了满足弱消去律的拟内射模;证明了素的正则右自内射环上的任意非奇异内射右R-模可以从直和项中弱消去.  相似文献   

2.
T拟内射模与TQI环   总被引:2,自引:0,他引:2  
张顺华 《数学学报》1995,38(1):71-76
本文定义并刻划了T拟内射模与T拟内射包,证明了WG-cocriticalT拟内射模的自同态环为正则非奇异右自内射环.最后讨论了T拟内射模与T内射模一致的环,即TQI环.还给出了Gabriel拓扑G中每个右理想T拟内射的几个等价条件  相似文献   

3.
正则环上的幂问题   总被引:3,自引:0,他引:3  
陈焕艮  佟文廷 《数学学报》1997,40(6):815-822
本文研究了正则环上模的幂消去,得到了幂消去的内直和刻划.建立了正则环上的幂比较结构,从而给出了正则环上幂消去、幂的弱消去以及u-正则性之间的关系  相似文献   

4.
关于环的极大本质右理想   总被引:7,自引:0,他引:7  
设R为环,我们考虑下面两个条件。(*)R的每个极大本质右理想是GP-内射右R-模或右零化子.(*)R的每个极大本质右理想是YJ-内射右R-模.本文旨在研究满足条件(*)或(*)的环,同时我们还给出了强正则环和除环的一些新刻画.  相似文献   

5.
广义FP—内射模、广义平坦模与某些环   总被引:2,自引:0,他引:2  
左(右)R-模A称为GFP-内射模,如果ExtR(M,A)=0对任-2-表现R-模M成立;左(右)R-模称为G-平坦的,如果Tor1^R(M,A)=0(Tor1^R(AM)=0)对于任一2-表现右(左)R-模M成立;环R称左(右)R-半遗传环,如果投射左(右)R-模的有限表现子模是投射的,环R称为左(右)G-正而环,如果自由左(右)R-模的有限表现子模为其直和项,研究了GFP-内射模和G-平坦模的一些性质,给出了它们的一些等价刻划,并利用它们刻划了凝聚环,G-半遗传环和G-正则环。  相似文献   

6.
关于半交换环与强正则环   总被引:1,自引:0,他引:1  
本文得到了环R是强正则环的若干充分必要条件,证明了下面条件是等价的:(1)R是强正则的;(2)R是半交换正则的;(3)R是半交换的左SF-环;(4)R是半交换的ELT环,且使得每个单左R-模是P-内射的或者平坦的;(5)R是半交换右非奇异的左SF-环;(6)R是半素的半交换左(或右)P-内射环.  相似文献   

7.
引入了弱直投射和弱直内射模的概念,给出了它们的一些性质。使用弱直投射和弱直内射模刻划了遗传环、半遗传环、半单环和QF-环。  相似文献   

8.
黎奇升  佟文廷 《数学学报》2002,45(6):1121-112
本文研究模的弱消去问题和exchange环的弱稳定条件,给出了wsrl条件的新刻划,证明了对具有有限exchange性质的模,外弱消去等价于内弱消去并等价于自同态环满足wsrl条件.  相似文献   

9.
一类广义遗传环   总被引:2,自引:0,他引:2  
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。  相似文献   

10.
陈建龙 《数学季刊》1992,7(1):25-31
本文主要证明了:(1)适合右零化子升链条件的左A-内射环为QF环。(2)适合左零化子升链条件的左f-内射环为QF环。(3)若对环R的任意左理想A,B和右理想I满足r(A∩B)=r(A) r(B),rι(I)=I,则R为半完全环且有本质左基座,特别地,右CF的左A-内射环(或E(RR)为投射左R-模)为QF环。  相似文献   

11.
The notion of weak comparability was first introduced by K.C. O’Meara, to prove that directly finite simple regular rings satisfying weak comparability must be unit-regular. In this paper, we shall treat (non-necessarily simple) regular rings satisfying weak comparability and give some interesting results. We first show that directly finite regular rings satisfying weak comparability are stably finite. Using the result above, we investigate the strict cancellation property and the strict unperforation property for regular rings satisfying weak comparability, and we show that these rings have the strict unperforation property, which means that nAnB implies AB for any finitely generated projective modules A, B and any positive integer n.   相似文献   

12.
We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O'Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and -algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules.

  相似文献   


13.
We are interested in (right) modules M satisfying the following weak divisibility condition: If R is the underlying ring, then for every r ∈ R either Mr = 0 or Mr = M. Over a commutative ring, this is equivalent to say that M is connected with regular generics. Over arbitrary rings, modules which are “minimal” in several model theoretic senses satisfy this condition. In this article, we investigate modules with this weak divisibility property over Dedekind-like rings and over other related classes of rings.  相似文献   

14.
Mamoru Kutami 《代数通讯》2013,41(5):1579-1593
We study regular rings satisfying generalized almost comparability. First, we determine the forms of regular rings satisfying generalized almost comparability. Next, using the above result, we treat the strict cancellation property and the strict unperforation property for regular rings satisfying generalized almost comparability.  相似文献   

15.
Mamoru Kutami 《代数通讯》2013,41(7):2171-2182
In this article, we study regular rings satisfying almost comparability. We first show that, for regular rings, almost comparability is inherited by finitely generated projective modules and finite matrix rings, and, as a main result, we prove that the strict cancellation property holds for the family of all finitely generated projective modules over directly finite regular rings satisfying almost comparability.  相似文献   

16.
陈焕艮  秦厚荣 《数学学报》2004,47(2):389-392
本文得到了相关比较Exchange环上模的替代性,并研究了幂比较Exchange 环上模的结构,进而提供了一类新的相关比较:Exchange环.  相似文献   

17.
The Comparable Structure of Exchange Rings   总被引:1,自引:0,他引:1  
We obtain a new substitution for modules over exchange rings satisfying related comparability. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability. Received June 1, 1998, Revised November 15, 1999, Accepted June 1, 2000  相似文献   

18.
A right R-module satisfies the right Beachy–Blair condition if each of its faithful submodules is cofaithful. In this article we study the relationship between the right Beachy–Blair condition of a right R-module and its skew polynomial, skew monoid and skew generalized power series extensions. Consequently, several known results regarding rings satisfying the right Beachy–Blair condition are extended to a more general setting.  相似文献   

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