Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter May 17, 2006

Tilting modules and Gorenstein rings

Lidia Angeleri Hügel, Dolors Herbera and Jan Trlifaj
From the journal

Abstract

We apply tilting theory to study modules of finite projective dimension. We introduce the notion of finite and cofinite type for tilting and cotilting classes of modules, respectively, showing that, for each dimension, there is a bijection between these classes and resolving classes of modules.

We then focus on Iwanaga-Gorenstein rings. Using tilting theory, we prove the first finitistic dimension conjecture for these rings. Moreover, we characterize them among noetherian rings by the property that Gorenstein injective modules form a tilting class. Finally, we give an explicit construction of families of (co)tilting modules of (co)finite type for one-dimensional commutative Gorenstein rings.


(Communicated by Rüdiger Göbel)

Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday


Received: 2004-06-08
Accepted: 2004-08-02
Published Online: 2006-05-17
Published in Print: 2006-03-21

© Walter de Gruyter

Scroll Up Arrow