Tilting theory and the finitistic dimension conjectures

Author:

Angeleri-Hügel Lidia,Trlifaj Jan

Abstract

Let R R be a right noetherian ring and let P > \mathcal {P}^{>\infty } be the class of all finitely presented modules of finite projective dimension. We prove that findim R = n > R = n > \infty iff there is an (infinitely generated) tilting module T T such that pd T = n T = n and T = ( P > ) T ^\perp = (\mathcal P^{>\infty })^\perp . If R R is an artin algebra, then T T can be taken to be finitely generated iff P > \mathcal P^{>\infty } 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference20 articles.

1. Infinitely generated tilting modules of finite projective dimension;Angeleri Hügel, Lidia;Forum Math.,2001

2. L. Angeleri Hügel, F. U. Coelho, Infinitely generated complements to partial tilting modules, Math. Proc. Cambridge Philos. Soc. 132 (2002), 88–95.

3. Tilting preenvelopes and cotilting precovers;Angeleri Hügel, Lidia;Algebr. Represent. Theory,2001

4. Functors and morphisms determined by objects;Auslander, Maurice,1978

5. Applications of contravariantly finite subcategories;Auslander, Maurice;Adv. Math.,1991

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