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Indecomposable pure-injective objects in stable categories of Gorenstein-projective modules over Gorenstein orders (2209.15630v1)
Published 30 Sep 2022 in math.AC, math.CT, math.RA, and math.RT
Abstract: We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order is of finite Cohen-Macaulay representation type if and only if every indecomposable pure-injective object in the stable category of Gorenstein-projective modules is compact.