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1.
Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω.  相似文献   

2.
In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.  相似文献   

3.
In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries.  相似文献   

4.
We prove that the regularity of a vertex operator superalgebra can be reduced to the semisimplicity of the category of its weak modules.Moreover,the rationality can be replaced by requiring that each 1/2Z+-graded module is a direct sum of irreducible weak modules.  相似文献   

5.
For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.  相似文献   

6.
尚文亮 《数学季刊》2012,(3):389-396
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.  相似文献   

7.
This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.We show this dimension has nice properties when the ring is coherent,and extend the well-known Hilbert's syzygy theorem to the strongly Gorenstein flat dimensions of rings.Also,we investigate the strongly Gorenstein flat dimensions of direct products of rings and(almost)excellent extensions of rings.  相似文献   

8.
Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i (Ext^i (-, U), U) preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension.  相似文献   

9.
王晓荣  陈建龙 《东北数学》2008,24(5):409-422
In this paper, the "relative" version of semi-projectivity is considered. Let M and N be modules. N is called M-semi-projective, if any homomorphism from N to an M-eyclie submodule f(M) of N can be factored through to a homomorphism from N to M and f, where f∈[M, N]. Some properties of relative semi-projectivity are obtained. Next, we consider a wider class of "elatively semi-projective" modules such as "elatively direct-projective" modules which were introduced by Nicholson and Zhou. Several properties of their homomorphisms are also obtained.  相似文献   

10.
关于有理模和余理想子代数的性质   总被引:1,自引:0,他引:1  
张良云 《东北数学》2000,16(3):265-271
In this paper, for some used conceptions and notations, we see [1] and [2].§1. Rational Module and Its Exact Sequence In [1], Cai Chuanreng and Cheng Huixiang have proved that relative Hopf modules and rational modules are one by one corresponding. In [2], Zhang Liangyun has given the dual relationship between relative Hopf modules. Naturally, we have a question to ask: is the dual module of a rational module still a rational module? This answer is affirmative. Let H be a Hopf …  相似文献   

11.
《代数通讯》2013,41(5):1303-1314
Abstract

We define some numerical invariants over Cohen–Macaulay local rings. These invariants are related to columns of the presenting matrices of maximal Cohen–Macaulay modules and syzygy modules without free summands. We study the relationship between these invariants, and the invariant col(A).

  相似文献   

12.
We present a constructive solution of the inverse syzygy problem over arbitrary coherent rings. By relating the existence of a kernel representation to torsionlessness instead of the more common torsionfreeness, we do not need to assume the existence of a quotient field. As a by-product, we obtain an algorithm to compute the extension groups of finitely presented modules.  相似文献   

13.
This paper aims at generalizing the notions of “Auslander dual”, “k-torsionless” and “k-th syzygy” modules to the relative setting with respect to a semidualizing module. It is shown that the “relative” Auslander dual shares many nice properties with the Auslander dual originally introduced by Auslander and Bridger. It is also shown the interplay between the “relative” version of “k-torsionless” and “k-th syzygy” modules parallels that of k-torsionless and k-th syzygy modules.  相似文献   

14.
Huang Zhaoyong 《代数通讯》2013,41(3):1457-1464
Let Λ be a left and right Noetherian ring. For a positive integer k, we give an equivalent condition that flat dimensions of the first k terms in the minimal injective resolution of Λ are less than or equal to k. In this case we show that the subcategory consisting of k-torsionfree modules is extension closed. Moreover we prove that for a Noetherian algebra every subcategory consisting of i-torsionfree modules is extension closed for any 1 ≤ ik if and only if every subcategory consisting of i-th syzygy modules is extension closed for any 1 ≤ ik. Our results generalize the main results in Auslander and Reiten [4].  相似文献   

15.
扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.  相似文献   

16.
张良云  祝家贵  佟文廷 《数学学报》2003,46(6):1143-115
本文引入了扭曲余模概念,给出了由扭曲余模构造的扭曲Hopf模的判别条件及其基本结构定理,引入了相关Yetter-Drinfel’d模概念(它是Yetter-Drinfel’d模概念的自然推广),证明了相关Yetter-Drinfel’d模范畴是预辫monoidal范畴,指出了由Yetter-Drinfel’d模通过扭曲余模构作的模恰是相关Yetter-Drinfel’d模.  相似文献   

17.
Liang Yan  Weiqing Li 《代数通讯》2013,41(2):591-603
Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting modules in relative homological algebra considering subfunctors of the Ext-functor. In this article we generalize Auslander–Solberg relative notions by giving the definitions of infinitely generated Gorenstein cotilting and tilting modules by means of Gorenstein exact sequences. Using the theory developed by Enochs on the existence of Gorenstein preenvelopes and precovers, we prove a characterization of relative Gorenstein cotilting and tilting modules, which is a generalization of the beautiful characterization of relative cotilting and tilting modules given by Bazzoni.  相似文献   

18.
《Journal of Algebra》2006,295(1):179-194
Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.  相似文献   

19.
Every finitely generated rank 2 third syzygy module over a regular local ring is known to be self-dual. We show more generally that any finitely generated rank 2 reflexive module is self-dual, and that the isomorphism is skew symmetric. We use this ismorphism to estimate how large k may be if the module is a kth syzygy, and how closely allied rank 3 modules are related to their duals.  相似文献   

20.
Campanella's refinements of Dubreil's theorem are sharp upper and lower bounds, formulated in postulational terms, for the number of forms of any given degree in the standard bases of 2-codimensional perfect homogeneous polynomial ideals. This note considers the implications of upper-bound-extremality. Its principal discovery is that such extremality implies a splitting of the syzygy module of any standard basis of such an ideal into syzygy modules of the standard bases of ‘component’ ideals explicitly describable in terms of the standard basis in question.  相似文献   

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