A note on relative tilting modules

Bazzoni had given a simple characterization of infinitely generated nn-tilting modules. Though her method is even inapplicable to classical nn-tilting modules over Artin algebras, we show in this note that a similar characterization does hold for (finitely generated) relative nn-tilting modules introduced by Auslander and Solberg for Artin algebras, by using a different method. We also present some applications.