Tilting Modules and the Subcategories (C^M_i)

Abstract

In this article we further study the full subcategories of the category of finitely generated modules over an Artin algebra introduced in Platzeck and Pratti (2000), consisting of the modules having an add M resolution of length i, which remains exact under the functor Hom _A (M, −). In particular, we characterize tilting modules in terms of these categories and determine when the transpose of a tilting module is a tilting module.

ACKNOWLEDGMENTS

The authors gratefully acknowledge partial support from Universidad Nacional del Sur and from CONICET, in Argentina. The first author is a researcher at CONICET.

Notes

Communicated by M. Ferrero.