An Auslander-Type result for Gorenstein-projective modules

• Autores: Xiao-Wu Chen
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 6, 2008, págs. 2043-2050
• Idioma: inglés
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• Resumen

  • 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 [M. Auslander, A functorial approach to representation theory, in: Representations of Algebras, Workshop Notes of the Third Internat. Conference, in: Lecture Notes in Math., vol. 944, Springer-Verlag, Berlin, 1982, pp. 105�179; M. Auslander, Representation theory of artin algebras II, Comm. Algebra (1974) 269�310]