Minimal silting modules and ring extensions

Minimal silting modules and ring extensions

Ring epimorphisms often induce silting modules and cosilting modules, termed minimal silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra. In particular, we show that a large cotilting m...

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Veröffentlicht in:Science China. Mathematics 2022-09, Vol.65 (9), p.1775-1794
Hauptverfasser: Hügel, Lidia Angeleri, Cao, Weiqing
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Applications of Mathematics
Homology
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
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description Ring epimorphisms often induce silting modules and cosilting modules, termed minimal silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra. In particular, we show that a large cotilting module is minimal if and only if it has an adic module as a direct summand. Secondly, we discuss the behavior of minimality under ring extensions. We show that minimal cosilting modules over a commutative noetherian ring extend to minimal cosilting modules along any flat ring epimorphism. Similar results are obtained for commutative rings of small homological dimension.
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subjects Applications of Mathematics
Homology
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
title Minimal silting modules and ring extensions
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