Tilting modules and universal localization. (Q2905090)

The article shows that every tilting module of projective dimension one over a ring \(R\) is associated to the universal localization \(R\to R_{\mathfrak U}\) at a set \(\mathfrak U\) of finitely presented modules of projective dimension one. This result is the extension of Gabriel's and de la Pena's results about association of tilting module \(T\) of projective dimension one over ring \(R\) and a ring epimorphism \(\lambda\colon R\to S\). Tilting modules of the form \(R_{\mathfrak U}\oplus R_{\mathfrak U}/R\) are discussed. Furthermore, the relationship between universal localization and the localization \(R\to Q_{\mathcal G}\) given by a perfect Gabriel topology \(\mathcal G\). In particular it is observed that if \(R\) is semihereditary, then every perfect localization \(R\to G_{\mathcal G}\) arises from universal localization at a set of finitely presented modules. Finally, some application to Artin algebras and to Prüfer domains is given.