We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R_U of R at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form R_U \oplus R_U/R, and we discuss the relationship between R_U and the localization given by a perfect Gabriel topology. Finally,we give some applications to Artin algebras and to Prüefer domains.
Tilting modules and universal localization
ANGELERI, LIDIA;
2012-01-01
Abstract
We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R_U of R at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form R_U \oplus R_U/R, and we discuss the relationship between R_U and the localization given by a perfect Gabriel topology. Finally,we give some applications to Artin algebras and to Prüefer domains.
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