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1.
模的嵌入问题   总被引:1,自引:0,他引:1  
本文首先在文[1]工作的基础上进一步讨论了“每个有限生成模可嵌入到自由模”的环类,这类环称为FGF-环,接着引进了一类包括FGF-环和拟完全环的环类,这类环称作FGFF-环,即“每个有限生成平坦模可嵌入到自由模中”,讨论了这类环的一些特征性质及其与已知一些重要环类间的关系.这一类环的背景是文[1-6].本文还回答了文[5]的一个问题.  相似文献   

2.
对交换环R和B-模范畴上的一个内射余生成元B,我们用相对于E的对偶模的性质刻画了QF环,IF环和半遗传环.  相似文献   

3.
利用模丛之间的嵌入关系,构造出了自由丛 的嵌入子丛和任一模丛的嵌入子自由丛. 得到一般模丛都能够成为一个自由丛 的嵌入子丛; 同时任一模丛也能够有一自由丛(或投射丛)是它的嵌入子丛; 还给出了投射丛转化为自由丛的条件.  相似文献   

4.
本文利用模的H-有限生成性质刻画了具有性质任意有限生成左模是自由模的子模的环.另外,还给出了左IF-环的一个刻画.  相似文献   

5.
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   

6.
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   

7.
设R为环,t是左R-模范畴的一个遗传挠理论.文中证明了下述各点等价:(1)每个内射左R-模是t-平坦的;(2)每个t-有限表现左R-模的内射包络是t-平坦的;(3)每个t-有限表现左R-模是自由R-模的子模;(4)每个t-有限表现左R-模是自反的且其对偶模是H-有限生成的.  相似文献   

8.
对Kay-Moody代数g′上的任意可积模(V,dπ),通过指数可以把它提升为同g′关联的Kac-Moody群G上的模(V,π),G上的这种模称为可微分模.本文将刻画G上的可微分模并且证明,模(V,π)是可微分模当且仅当V到每个根子群U的限制都是U的一个有理表示.依据这种刻画,得到一个有趣的结果:有理数域Q上的Chevaley群G(Q)的所有有限维模都是可微分模  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  
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   

10.
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   

11.
几乎余挠模     
毛立新 《东北数学》2006,22(1):67-72
In this paper, we introduce the concept of almost cotorsion modules. A module is called almost cotorsion if it is subisomorphic to its cotorsion envelope. Some characterizations of almost cotorsion modules are given. It is also proved that every module is a direct summand of an almost cotorsion module. As an application, perfect rings are characterized in terms of almost cotorsion modules.  相似文献   

12.
S-内射模及S-内射包络   总被引:1,自引:0,他引:1  
设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模.  相似文献   

13.
Lu Bo  Liu Zhongkui 《代数通讯》2013,41(2):361-374
In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial generalization of flat (resp., injective) modules. We investigate the properties of these modules in various ways. For example, we show that the class of IFP-flat (resp., IFP-injective) modules is closed under direct products and direct sums. Therefore, the direct product of flat modules is not flat in general; however, the direct product of flat modules is IFP-flat over any ring. We prove that (??, ??) is a complete cotorsion theory and (??, ??) is a perfect cotorsion theory, where ?? stands for the class of all IFP-injective left R-modules, and ?? denotes the class of all IFP-flat right R-modules.  相似文献   

14.
A submodule N of a module M is idempotent if N = Hom(M, N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized.  相似文献   

15.
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of g-static modules is closed under the kernels.  相似文献   

16.
Jiaqun Wei 《代数通讯》2013,41(5):1817-1829
We introduce the notion of ω-Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective modules and Gorenstein injective modules. We consider such modules in the tilting theory. Consequently, some results due to Auslander and colleagues and Enochs and colleagues are generalized.  相似文献   

17.
Rachid Tribak 《代数通讯》2013,41(12):4448-4460
We say that a module M is lifting if M is amply supplemented and every supplement submodule of M is a direct summand. The module M is called cofinitely lifting if it is amply cofinitely supplemented and every supplement of any cofinite submodule of M is a direct summand. In this article various properties of cofinitely lifting modules are given. In addition, a generalization of cofinitely lifting modules is investigated.  相似文献   

18.
A characterization of finitely generated torsion modules of not necessarily finite projective dimension over a Cohen–Macaulay ring, is given in terms of the non-Cohen–Macaulay loci and the Fitting invariants of a free resolution of such a module.  相似文献   

19.
We introduce generalizations of extending modules and lifting modules relative to proper classes of short exact sequences of modules, and we characterize modules for which any direct sums of copies of them are such relative extending modules or relative lifting modules.  相似文献   

20.
Ziqun Lu 《代数通讯》2013,41(9):2753-2766
We determine the multiplicity algebras and multiplicity modules of a p-monomial module. For a general p-group P, we find a sufficient and necessary condition for an endo-monomial P-module to be an endo-permutation P-module, and prove that a capped indecomposable endo-monomial P-module is of p -rank. At last, we give an alternative definition of the generalized Dade P-group.  相似文献   

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