共查询到19条相似文献,搜索用时 122 毫秒
1.
1984年,Ho Kuen Ng在[1]中给出了交换环与模的有限表现维数(简称为F.P.—维数)的定义及若干有意义的重要结果.从此,有限表现性的讨论成为环论的热门课题之一.作者在[2]中将有限表现维数推广到非交换环上.并利用有限表现维数刻划了凝聚环,在[3]中讨论了有限表现维数的换环定理.在[4]中讨论了笛卡尔方形上的有限表现维数.丁南庆在[5]中推广了有限表现维数,给出了一种新维数——模的有限生成维数,在[6]中讨论了有限表现模的对偶 相似文献
2.
有限表现维数与凝聚环 总被引:1,自引:0,他引:1
在本文中,我们从研究投射等价模的有限表现维数的关系入手,给出了有限表现维数的维数转移定理(定理2.5),并且运用有限表现维数刻划了凝聚环(定理2.4)。最后我们得到了在经典局部化下,环与模的有限表现维数的不变性定理(定理2.6,定理2.8)。 相似文献
3.
4.
一类Morita Contexts的M-投射左总体维数 总被引:1,自引:0,他引:1
我们引进了模的M-投射维数和环的M-左总体维数的概念,采用比较新颖简便的方法,得到了一类Morita Contexts T=R ReeR eRe,e∈R,e2=e和环的M-左总体维数之间的相等关系. 相似文献
5.
6.
7.
8.
9.
10.
引入了左R-模M关于可解模类X以及内射余生成子W的同调维数.给出了M的X-分解维数有限的几种刻画,进而讨论了M的这两种维数之间的关系.研究了相对于有限W-分解维数的模的稳定性以及相对于模类X的模的稳定性. 相似文献
11.
引入了弱投射模及弱投射维数的概念,说明弱投射模是FP-投射模的真子类.给出了环的整体弱投射维数的刻画,并得到了凝聚环和Noether的一些新的同调刻画. 相似文献
12.
《代数通讯》2013,41(11):4415-4432
Abstract Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper, we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. Moreover a characterization of Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings is given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions. 相似文献
13.
Let , ? be classes of modules, we introduce and characterize orthogonal dimensions of modules and rings by the orthogonal classes of modules ⊥, ⊥ ?, and T . For an almost excellent extension S ≥ R, we give the criteria to test some identities of orthogonal dimensions of modules and rings. As corollaries, some known results are obtained or extended. 相似文献
14.
M. Davoudian 《代数通讯》2013,41(9):3907-3917
We introduce and study the concept of dual perfect dimension which is a Krull-like dimension extension of the concept of acc on finitely generated submodules. We observe some basic facts for modules with this dimension, which are similar to the basic properties of modules with Noetherian dimension. For Artinian serial modules, we show that these two dimensions coincide. Consequently, we prove that the Noetherian dimension of non-Noetherian Artinian serial modules over the rings of the title is 1. 相似文献
15.
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
16.
耿玉仙 《数学物理学报(B辑英文版)》2010,30(4):1029-1043
Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic. 相似文献
17.
John Koker 《Georgian Mathematical Journal》1995,2(4):419-424
Recently, there have been many results which show that the global dimension of certain rings can be computed using a proper subclass of the cyclic modules, e.g., the simple modules. In this paper we view calculating global dimensions in this fashion as a property of a ring and show that this is a property which transfers to the ring's idealizer and subidealizer ring. 相似文献
18.
A left R-module M is called strongly P-projective if Exti(M, P) = 0 for all projective left R-modules P and all i ≥ 1. In this article, we first discuss properties of strongly P-projective modules. Then we introduce and study the strongly P-projective dimensions of modules and rings. The relations between the strongly P-projective dimension and other homological dimensions are also investigated. 相似文献
19.
本文用模的自同态,给出弱总体维数≤n的环的特征,其中n≥0.设R为环,部分地回答了下列问题:何时任意有限表现R-模M有无穷分解:0→M→F0→F1→…→Fn→…,其中每个Fi均是有限生成投射的,i=1,2,…? 相似文献