An Auslander-type result for Gorenstein-projective modules

Details An Auslander-type result for Gorenstein-projective modules An Auslander-type result for Gorenstein-projective modules

2007-09-21

arxiv.org/abs/0709.3452v2

Advances in Mathematics, 218 (2008), 2043-2050.

Mathematics

Representation Theory

Comments are welcome. Adv. Math., accepted

Scientific paper

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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