Tilting theory and the finitistic dimension conjectures

Lidia Angeleri-Hügel, Jan Trlifaj

Research output: Contribution to journalArticleResearchpeer-review

31 Citations (Scopus)

Abstract

Let R be a right noetherian ring and let Plt;∞ be the class of all finitely presented modules of finite projective dimension. We prove that findimR = n < ∞ iff there is an (infinitely generated) tilting module T such that pdT = n and T⊥ = (P<∞)⊥. If R is an artin algebra, then T can be taken to be finitely generated iff P<∞ is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø.
Original languageEnglish
Pages (from-to)4345-4358
JournalTransactions of the American Mathematical Society
Volume354
Issue number11
DOIs
Publication statusPublished - 1 Nov 2002

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