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Let R be a complete local Gorenstein ring of dimension one, with maximal ideal 𝔪 $\mathfrak {m}$ . 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 $\mathfrak {m}$ corresponding to a minimal prime ideal of R. We apply this result to determining the shape of some components of stable Auslander-Reiten quivers, which in the considered examples are shown to be tubes.
Algebras and Representation Theory – Springer Journals
Published: May 30, 2018
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