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Universal localizations via silting

Part of: Homological methods Rings and algebras arising under various constructions Abelian categories

Published online by Cambridge University Press:  27 December 2018

Frederik Marks  and
Jan Št'ovíček
Frederik Marks
Affiliation:
University of Stuttgart, Institute for Algebra and Number Theory, Pfaffenwaldring 57, 70569 Stuttgart, Germany ([email protected])
Jan Št'ovíček
Affiliation:
Faculty of Mathematics and Physics, Department of Algebra, Charles University in Prague, Sokolovská 83, 186 75 Praha, Czech Republic ([email protected])
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Abstract

We show that silting modules are closely related with localizations of rings. More precisely, every partial silting module gives rise to a localization at a set of maps between countably generated projective modules and, conversely, every universal localization, in the sense of Cohn and Schofield, arises in this way. To establish these results, we further explore the finite-type classification of tilting classes and we use the morphism category to translate silting modules into tilting objects. In particular, we prove that silting modules are of finite type.

Keywords

Universal localizationsilting moduletilting modulering epimorphism

MSC classification

Primary: 16S85: Rings of fractions and localizations 18E40: Torsion theories, radicals
Secondary: 16E30: Homological functors on modules (Tor, Ext, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 2 , April 2019 , pp. 511 - 532
Copyright
Copyright © Royal Society of Edinburgh 2018 

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