منابع مشابه
The existence totally reflexive covers
Let $R$ be a commutative Noetherian ring. We prove that over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.
متن کاملBeyond Totally Reflexive Modules and Back A Survey on Gorenstein Dimensions
Lars Winther Christensen, Hans-Bjørn Foxby, and Henrik Holm 1 Department of Mathematics and Statistics, Texas Tech University, Mail Stop 1042, Lubbock, TX 79409, U.S.A. [email protected] 2 Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark [email protected] 3 Department of Basic Sciences and Environment, University of Copenh...
متن کاملTotally reflexive extensions and modules
Article history: Received 23 August 2012 Available online xxxx Communicated by Luchezar L. Avramov MSC: 16G50 13B02 16E65
متن کاملTilting Selfinjective Algebras and Gorenstein Orders
BY Rickard's fundamental theorem [8], the rings which are derived equivalent to a ring A are precisely the endomorphism rings of tilting complexes over A. A tilting complex T is a finitely generated complex of finitely generated projective modules, which does not admit selfextensions and which has the property that the smallest triangulated subcategory of D(A) which contains T also contains all...
متن کاملBrauer–thrall for Totally Reflexive Modules
Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R, m) with m3 = 0 are commonly regarded as the stru...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.12.021