Abstract

An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by Auslander's idea on representation dimension, we prove that for 2 ⩽ n < ∞ , A is a CM-finite n-Gorenstein algebra if and only if there is a resolving Gorenstein-projective A-module E such that gl.dim End A ( E ) op ⩽ n .

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