An Auslander-type result for Gorenstein-projective modules

Xiao-Wu Chen

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arXiv · 0709.3452

An Auslander-type result for Gorenstein-projective modules

Xiao-Wu Chen

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Abstract

An artin algebra $A$ is said to be CM-finite if there are only finitely many, up to isomorphisms, indecomposable finitely generated Gorenstein-projective $A$-modules. We prove that for a Gorenstein artin algebra, it is CM-finite if and only if every its Gorenstein-projective module is a direct sum of finitely generated Gorenstein-projective modules. This is an analogue of Auslander's theorem on algebras of finite representation type (\cite{A,A1}).

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BibTeX RIS

Xiao-Wu Chen. 2008-04-07. An Auslander-type result for Gorenstein-projective modules. https://arxiv.org/abs/0709.3452

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