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 共查询到19条相似文献,搜索用时 78 毫秒
1.
邓培民 《应用数学》1998,11(3):114-117
本文首先介绍了co-*-模的概念和刻划了凝聚环的一些性质,然后刻划了凝聚环上的cotilting模。  相似文献   

2.
利用几乎有限表现模来刻划凝聚环和半遗传环.通过讨论几乎有限表现模和广义有限表现模之间的关系,得出了几个关于几乎有限表现模和凝聚环、半遗传环的等价条件,改进了已有的结论,把刻划凝聚环的模缩小到几乎有限表现模.  相似文献   

3.
凝聚环和IF环   总被引:2,自引:0,他引:2  
朱晓胜 《数学学报》1997,40(6):845-852
本文利用特征模,N0-内射维数对凝聚环给出了一些新的刻划.得到了凝聚环与IF环的一些有意义的性质.推广了引文[1]中的两个主要定理之一的定理2的结论.  相似文献   

4.
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   

5.
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   

6.
模的弱消去问题与qu-正则环   总被引:3,自引:1,他引:3  
武同锁 《数学学报》1995,38(6):746-751
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   

7.
特征模对环的刻划   总被引:4,自引:1,他引:4  
朱晓胜 《数学学报》1996,39(6):743-750
设R是一个环,M是一个左R摸,M*=HomZ(M,Q/Z)为M的特征模.R.R.Colby和T.J.Choathan等人利用特征模对IF环、凝聚环、Noether环、Artin环作出了一些非常好的刻划.本文利用特征模对更为广泛的一些环作出了较有意义的刻划.  相似文献   

8.
右IF-环及凝聚环的挠理论   总被引:2,自引:0,他引:2  
张力宏 《数学学报》1995,38(1):117-126
本文研究了右IF-环的性质,证明出环R是右IF-环当且仅当R是左凝聚环,并且是平坦模;由此证明出右IF-环与左GQF-环是等价的,其次应用右IF-环研究了凝聚环的挠理论性质,证明出凝聚环与T-凝聚环的关系。  相似文献   

9.
右IF-环及凝聚环的挠理论   总被引:2,自引:0,他引:2  
本文研究了右IF-环的性质,证明出环R是右IF-环当且仅当R是左凝聚环,并且是平坦模;由此证明出右IF-环与左GQF-环是等价的,其次应用右IF-环研究了凝聚环的挠理论性质,证明出凝聚环与T-凝聚环的关系。  相似文献   

10.
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   

11.
In this paper, we generalize the characterization of Gorenstein flat modules over Gorenstein rings to n ? FC rings (coherent rings with finite sdf?FP?injective dimension), and characterize n ? FC rings in terms of Gorenstein flat and projective modules.  相似文献   

12.
《代数通讯》2013,41(12):6149-6159
Abstract

A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and Π-coherent rings with property (P).  相似文献   

13.
Driss Bennis 《代数通讯》2013,41(3):855-868
A ring R is called left “GF-closed”, if the class of all Gorenstein flat left R-modules is closed under extensions. The class of left GF-closed rings includes strictly the one of right coherent rings and the one of rings of finite weak dimension.

In this article, we investigate the Gorenstein flat dimension over left GF-closed rings. Namely, we generalize the fact that the class of all Gorenstein flat left modules is projectively resolving over right coherent rings to left GF-closed rings. Also, we generalize the characterization of Gorenstein flat left modules (then of Gorenstein flat dimension of left modules) over right coherent rings to left GF-closed rings. Finally, using direct products of rings, we show how to construct a left GF-closed ring that is neither right coherent nor of finite weak dimension.  相似文献   

14.
Let R be an associative ring with identity and F a class of R-modules. In this article: we first give a detailed treatment of Cartan-Eilenberg F complexes and extend the basic properties of the class F to the class CE(F). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes, including coherent, Noetherian, von Neumann regular rings, QF rings, semisimple rings, hereditary rings and perfect rings.  相似文献   

15.
Let R be a commutative ring and C a semidualizing R-module. We investigate the relations between C-flat modules and C-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.  相似文献   

16.
The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties of both classes of rings are closely related to the embedding of finitely presented modules in fp-flat and free modules, respectively. Using these properties, we characterize the classes of coherent CF- and FGF-rings. Moreover, it is proved that the group ring R(G) is FP-injective (weakly quasi-Frobenius, respectively) if and only if the ring R is FP-injective (weakly quasi-Frobenius) and G is locally finite. Bibliography: 15 titles.  相似文献   

17.
一、引言 设R是具有单位元的结合环,A为左(酉)R-模,则其对偶模A~*=Hom_R(A,R)是右R-模,依次可定义A~(**)=(A~*)~*等等。如众所知,任意环R上每个有限生成投射模之对偶模是投射的,但是,即使在Noether环上,并非每个投射模之对偶模是投射的。例如:F=Z是投射的Z-模,但是F~*=multiply form 1 to ∞(Z)不是投射Z-模(参阅[1])。一个自然的问题就是:何时投射(平坦或内射)模之对偶模是投射(平坦或内射)的?本文主要讨论这个问题。  相似文献   

18.
《代数通讯》2013,41(10):4811-4821
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.  相似文献   

19.
We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.  相似文献   

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