Tilting modules arising from ring epimorphisms

Lidia Angeleri Hügel, Javier Sánchez

    Research output: Contribution to journalArticleResearchpeer-review

    23 Citations (Scopus)

    Abstract

    We show that a tilting module T over a ring R admits an exact sequence 0→ R→T0→T1→0 such that T0, T1 ∈ Add(T) and HomR(T1, T0) = 0 if and only if T has the form S ⊕ S/R for some injective ring epimorphism λ R→ S with the property that Tor1R (S, S) = 0 and pdSR ≤ 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. © Springer Science + Business Media B.V. 2009.
    Original languageEnglish
    Pages (from-to)217-246
    JournalAlgebras and Representation Theory
    Volume14
    Issue number2
    DOIs
    Publication statusPublished - 1 Apr 2011

    Keywords

    • Dedekind domain
    • Hereditary noetherian prime ring
    • Ring epimorphism
    • Tilting module
    • Universal localization

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