Tilting Modules Arising from Ring Epimorphisms |
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Authors: | Lidia Angeleri Hügel Javier Sánchez |
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Institution: | 1.Dipartimento di Informatica e Comunicazione,Università degli Studi dell’Insubria,Varese,Italy;2.Departament de Matemàtiques,Universitat Autònoma de Barcelona,Barcelona,Spain |
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Abstract: | We show that a tilting module T over a ring R admits an exact sequence 0?→?R?→?T 0?→?T 1?→?0 such that \(T_0,T_1\in\text{Add}(T)\) and Hom R (T 1,T 0)?=?0 if and only if T has the form S?⊕?S/R for some injective ring epimorphism λ : R?→?S with the property that \(\text{Tor}_1^R(S,S)=0\) and pdS R ?≤?1. We then study the case where λ is a universal localization in the sense of Schofield (1985). Using results by Crawley-Boevey (Proc Lond Math Soc (3) 62(3):490–508, 1991), we give applications to tame hereditary algebras and hereditary noetherian prime rings. In particular, we show that every tilting module over a Dedekind domain or over a classical maximal order arises from universal localization. |
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