Auslander-Reiten conjecture and Auslander-Reiten duality

Published 28 Dec 2011 in math.AC | (1112.6201v3)

Abstract: Motivated by a result of Araya, we extend the Auslander-Reiten duality theorem to Cohen-Macaulay local rings. We also study the Auslander-Reiten conjecture, which is rooted in Nakayama's work on finite dimensional algebras. One of our results detects a certain condition that forces the conjecture to hold over local rings of positive depth.

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