An Auslander-type result for Gorenstein-projective modules
Chen, Xiao-Wu
arXiv, 0709.3452 / Harvested from arXiv
Text on arXiv
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}).
Publié le : 2007-09-21
Classification:  Mathematics - Representation Theory,  Mathematics - Rings and Algebras 
@article{0709.3452,
     author = {Chen, Xiao-Wu},
     title = {An Auslander-type result for Gorenstein-projective modules},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0709.3452}
}

Chen, Xiao-Wu. An Auslander-type result for Gorenstein-projective modules. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0709.3452/