Graded AR Sequences and the Huneke-Wiegand Conjecture

Abstract

We let R be a one-dimensional graded complete intersection, satisfying certain degree conditions which are satisfied whenever R is a numerical semigroup ring of embedding dimension at least three. We show that a graded maximal Cohen-Macaulay R-module M satisfies the Huneke-Wiegand Conjecture provided there exists an Auslander-Reiten sequence ending in M whose middle term has at least two nonfree direct summands.

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References in corpus (2)

• Symmetries and connected components of the AR-quiver
• Symmetry in the vanishing of Ext over Gorenstein rings

Cited by in corpus (1)

• The Huneke-Wiegand conjecture and middle terms of almost split sequences