Tilting Modules Arising from Ring Epimorphisms
By Lidia Angeleri Hugel, Javier Sánchez. 2008
49 citations recorded by the source corpus.
We show that a tilting module T over a ring R admits an exact sequence 0 → R → T0 → T1 → 0 such that $T_0,T_1\in\text{Add}(T)$ 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 $\text{Tor}_1^R(S,S)=0$ 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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2cccdea68120d21846bcf93bae61b148666582ee
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Citations in the corpus
- Recollements and tilting objects (2009, background): “classical tilting module (of projective dimension one); in this way we will extend results in [3] and put them into a general framework.”