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Tilting Modules Arising from Ring Epimorphisms

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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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Author notes

  1. Lidia Angeleri Hügel

    Present address: Dipartimento di Informatica - Settore di Matematica, Università di Verona, Strada le Grazie 15 - Ca’ Vignal 2, 37134, Verona, Italy

  2. Javier Sánchez

    Present address: Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP, 05508-090, Brazil

Authors and Affiliations

  1. Dipartimento di Informatica e Comunicazione, Università degli Studi dell’Insubria, Via Mazzini 5, 21100, Varese, Italy

    Lidia Angeleri Hügel

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella-terra, Barcelona, Spain

    Javier Sánchez

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  1. Lidia Angeleri Hügel
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  2. Javier Sánchez
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Correspondence to Lidia Angeleri Hügel.

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Angeleri Hügel, L., Sánchez, J. Tilting Modules Arising from Ring Epimorphisms. Algebr Represent Theor 14, 217–246 (2011). https://doi.org/10.1007/s10468-009-9186-x

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