Algebr Represent Theor https://doi.org/10.1007/s10468-018-9805-5 Auslander-Reiten Sequences for Gorenstein Rings of Dimension One Robert Roy Received: 14 September 2017 / Accepted: 22 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract 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 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. Keywords Commutative algebra · Auslander-reiten theory · Gorenstein Mathematics Subject Classification (2010) 13H10 · 16G70 1 Introduction The theory of Auslander-Reiten (AR) quivers is central in the study of artin algebras. Regarding AR theory for maximal Cohen-Macaulay modules over a complete Cohen- Macaulay local ring, the cases of finite AR quivers have been studied thoroughly (see ), but in the more common case of infinite type, shapes of AR quivers seem to be largely unknown. The paper  agrees with this assessment (cf. its introduction), and begins to bridge this gap. It establishes
Algebras and Representation Theory – Springer Journals
Published: May 30, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera