arXiv subjects

Robert Roy

Publications and source records attributed to Robert Roy.

2 recordsLinked to original sources

arXiv2018

Graded AR Sequences and the Huneke-Wiegand Conjecture

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.

math.AC↗

arXiv2017

Auslander-Reiten sequences for Gorenstein rings of dimension one

Let $R$ be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if $M$ is a Cohen-Macaulay $R$-module which begins an AR-sequence, then this sequence is produced by a particular endomorphism of m corresponding to a minimal prime ideal. We apply this result to determining the shape of some components of Auslander-Reiten quivers.

math.AC↗