Mathematisches Institut der Universität, Theresienstrasse 39, D-80333 München, Germany ; Katedra algebry MFF UK, Sokolovska'a 83, 186 75 Prague 8, Czech Republic
Abstract:
Let be a right noetherian ring and let be the class of all finitely presented modules of finite projective dimension. We prove that findim iff there is an (infinitely generated) tilting module such that pd and . If is an artin algebra, then can be taken to be finitely generated iff 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.