共查询到20条相似文献,搜索用时 144 毫秒
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熊涛 《纯粹数学与应用数学》2021,37(2):167-175
研究了Milnor方图上的余挠维数,然后探讨了环的余挠维数和整体维数,弱整体维数之间的关系和差别.证明了一个Prüfer整环的余挠维数不超过1当且仅当它是整体维数不超过2的Matlis整环. 相似文献
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在[1]中,作者讨论了有限整体维数的半局部环上有限生成非零模的同调维数和余维数的和的性质;定义了模N的次全维数(pro-total dimension)ptd_sN、次整体维数(pro-glo-bal dimension) pgd_sN,以及半局部环S本身的全维数 (total dimennsion)tdS;紧接着在§4讨论了上述各种维数之间的关系,然后在§6应用前面的结果去研究tdS=2的半局部环的结构。但我们发现[1]文中的某些结论不成立,本文试图举出[1]文中某些命题不成 相似文献
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n级三角矩阵环上的模范畴和同调特征 总被引:1,自引:0,他引:1
本文给出了n级三角矩阵环Гn的定义.证明了n级三角矩阵代数Гn上的有限生成模范畴mod Гn与范畴Гn(?)等价,得到了诸如Гn的Jacobson根,Гn(?)的不可分解投射对象的形式及Гn的整体维数等性质. 相似文献
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GCD整环与自反模 总被引:3,自引:0,他引:3
王芳贵 《数学年刊A辑(中文版)》1994,(2)
本文证明了凝聚整环是GCD整环当且仅当秩为1的自反模是自由模.同时还得到有限弱整体维数的凝聚整环是GCD整环当且仅当Pic(R)=1.特别地,有限整体维数的Noether整环是UFD当且仅当Pic(R)=1. 相似文献
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首次把有理同伦论中的同伦不变量-锥长度(cone length)引入到微分分次(简记为DG)同调代数中,定义了连通DG代数上DG模的锥长度.连通DG代数A的左(右)整体维数定义为所有DGA-模(Aop-模)的锥长度的上确界.在一些特殊情形下,发现连通.DG代数A的左(右)整体维数与H(A)的整体维数有着密切的关系.任意一个连通分次代数,如果将它视为微分为O的连通DG代数,其左(右)整体维数与其作为连通分次代数的整体维数是一致的.因此该定义是连通分次代数整体维数的一种推广形式.证明A的整体维数足三角范畴D(A)以及Dc(A)的维数的一个上界.当A是正则DG代数时,给出了A的左(右)整体维数的一个有限上界. 相似文献
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Xiao-Wu Chen 《Algebras and Representation Theory》2009,12(2-5):181-191
We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz–Happel’s theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen–Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed. 相似文献
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Strongly Gorenstein Flat Modules and Dimensions 总被引:1,自引:0,他引:1
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We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-Calabi-Yau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite global dimension. Our results also apply to the stable (!) endomorphism rings of maximal rigid modules of [Christof Geiß, Bernard Leclerc, Jan Schröer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324, Invent. Math., in press]. In addition, we prove a general result about relative 3-Calabi-Yau duality over non-stable endomorphism rings. This strengthens and generalizes the Ext-group symmetries obtained in [Christof Geiß, Bernard Leclerc, Jan Schröer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324, Invent. Math., in press] for simple modules. Finally, we generalize the results on relative Calabi-Yau duality from 2-Calabi-Yau to d-Calabi-Yau categories. We show how to produce many examples of d-cluster tilted algebras. 相似文献
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We introduce the singularity category with respect to Ding projective modules, D_(dpsg)~b(R),as the Verdier quotient of Ding derived category D_(DP)~b(R) by triangulated subcategory K~b(DP), and give some triangle equivalences. Assume DP is precovering. We show that D_(DP)~b(R)≌K~(-,dpb)(DP)and D_(dpsg)~b(R)≌D_(Ddefect)~b(R). We prove that each R-module is of finite Ding projective dimension if and only if D_(dpsg)~b(R) = 0. 相似文献
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Dmitry Dubnov 《代数通讯》2013,41(9):4355-4374
We investigate finite dimensional 2-vertex basic algebras of finite global dimension and the derived categories of modules over such algebras. We prove that any superrigid object in the derived category of modules over a “loop-kind” two-vertex algebra is a pure module up to the action of Serre functor and translation. All superrigid objects in the derived categories of modules over two-vertex algebras of global dimension 2 are described. Also we obtain a complete classification of two-vertex basic algebras possessing a full exceptional pair in the derived category of modules. 相似文献
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《代数通讯》2013,41(4):2023-2035
ABSTRACT A Gorenstein module over a local ring R is a maximal Cohen–Macaulay module of finite injective dimension. We use existence of Gorenstein modules to extend a result due to S. Ding: A Cohen–Macaulay ring of finite index, with a Gorenstein module, is Gorenstein on the punctured spectrum. We use this to show that a Cohen–Macaulay local ring of finite Cohen–Macaulay type is Gorenstein on the punctured spectrum. Finally, we show that for a large class of rings (including all excellent rings), the Gorenstein locus of a finitely generated module is an open set in the Zariski topology. 相似文献
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Edgar E. Enochs Juan Martí nez Herná ndez Alberto del Valle 《Proceedings of the American Mathematical Society》1998,126(6):1611-1620
The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left module over such a ring has a flat cover (Belshoff, Enochs, Xu) and, if the weak global dimension is at most two, every left module has a flat envelope (Asensio, Martínez). We will exploit these features of this category to study its objects. In particular, we will consider orthogonal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we describe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the structure of the flat envelopes and of the ring itself.
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Florencio Castaño-Iglesias Constantin Năstăsescu Laura Năstăsescu 《Applied Categorical Structures》2013,21(2):105-118
We introduce for any Grothendieck category the notion of stable localizing subcategory, as a localizing subcategory that can be written as an intersection of localizing subcategories defined by indecomposable injectives. A Grothendieck category in which every localizing subcategory is stable is called a locally stable category. As a main result we give a characterization of these categories in terms of the local stability of a localizing subcategory and its quotient category. The locally coirreducible categories (in particular, the categories with Gabriel dimension) and the locally noetherian categories are examples of locally stable categories. We also present some applications to the category of modules over a left fully bounded noetherian ring, to the category of comodules over a coalgebra and to the category of modules over graded rings. 相似文献
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Houjun Zhang 《代数通讯》2020,48(2):467-483
AbstractIn this article, we investigate the Gorenstein global dimension with respect to the recollements of abelian categories. With the invariants spli and silp of the categories, we give some upper bounds of Gorenstein global dimensions of the categories involved in a recollement of abelian categories. We apply our results to some rings and artin algebras, especially to the triangular matrix artin algebras. 相似文献
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Maxim Vybornov 《代数通讯》2013,41(12):3985-3992
In this paper we study finite dimensional algebras arising from categories of perverse sheaves on finite regular cell complexes (cellular perverse algebras). We prove that such algebras are quasi-hereditary and have finite global dimension. We discuss some restrictions, under which cellular perverse algebras are Koszul. We also study the relationship between Koszul duality functors in the derived categories of categories of graded and non-graded modules over an algebra and its quadratic dual. 相似文献