Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
TILTING MODULES AND UNIVERSAL LOCALIZATION LIDIA ANGELERI HUGEL, MARIA ARCHETTI
 

Summary: TILTING MODULES AND UNIVERSAL LOCALIZATION
LIDIA ANGELERI H¨UGEL, MARIA ARCHETTI
Abstract. We show that every tilting module of projective dimen-
sion one over a ring R is associated in a natural way to the universal
localization R RU at a set U of finitely presented modules of pro-
jective dimension one. We then investigate tilting modules of the form
RU RU /R. Furthermore, we discuss the relationship between univer-
sal localization and the localization R QG given by a perfect Gabriel
topology G. Finally, we give some applications to Artin algebras and to
Pr¨ufer domains.
Introduction
Tilting modules of projective dimension one are often constructed via a
localization. For example, if is a left Ore set of regular elements in a ring
R with the property that the localization -1R is an R-module of projective
dimension at most one, then -1R-1R/R is a tilting right R-module, see
[1, 20, 21]. More generally, it was recently shown in [2] that every injective
homological ring epimorphism R S such that SR has projective dimension
at most one gives rise to a tilting R-module S S/R.
Note, however, that in general not all tilting modules arise as above from
an injective homological ring epimorphism. For example, if R is a commu-

  

Source: Angeleri Hügel, Lidia - Dipartimento di Informatica, Universita` di Verona

 

Collections: Mathematics