منابع مشابه
Totally reflexive extensions and modules
Article history: Received 23 August 2012 Available online xxxx Communicated by Luchezar L. Avramov MSC: 16G50 13B02 16E65
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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...
متن کاملThe 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 کاملTotally Reflexive Modules Constructed from Smooth Projective Curves of Genus
In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay normal domain and a nonfree totally reflexive module over it.
متن کاملOn the Number of Indecomposable Totally Reflexive Modules
In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2016
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2015.1130142