Abstract
We show that, over an Artin algebra, the tilting functor preserves (co)tilting modules in the subcategories associated to the functor. We also give a sufficient condition for the category of modules of finite projective dimensions over an Artin algebra to be contravariantly finite in the category of all finitely generated modules over the Artin algebra. This is a sufficient condition for the finitistic dimension of the Artin algebra to be finite (Auslander and Reiten in Adv Math 86(1), 1991).
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