2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169332An 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}).Comments are welcome. Adv. Math., acceptedRepresentation TheoryRings and Algebrastext