Auslander-Reiten components over pure-semisimple hereditary rings

Lidia Angeleri Hügel, Dolors Herbera

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri Hügel (2007) [2]. We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. © 2010 Elsevier Inc.
Original languageEnglish
Pages (from-to)285-303
JournalJournal of Algebra
Volume331
Issue number1
DOIs
Publication statusPublished - 1 Apr 2011

Keywords

  • Auslander-Reiten Theory
  • Cotilting duality
  • Pure-semisimple rings
  • Pure-Semisimplicity Conjecture
  • Tilting equivalence

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