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Minimal silting modules and ring extensions

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Abstract

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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Acknowledgements

The first author was supported by Fondazione Cariverona, Program “Ricerca Scientifica di Eccellenza 2018” (Project “Reducing Complexity in Algebra, Logic, Combinatorics — REDCOM”). The second author was supported by China Scholarship Council (Grant No. 201906860022).

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, Verona I, 37134, Italy

    Lidia Angeleri Hügel

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Weiqing Cao

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  1. Lidia Angeleri Hügel
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  2. Weiqing Cao
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Correspondence to Weiqing Cao.

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Hügel, L.A., Cao, W. Minimal silting modules and ring extensions. Sci. China Math. 65, 1775–1794 (2022). https://doi.org/10.1007/s11425-020-1898-6

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  • DOI: https://doi.org/10.1007/s11425-020-1898-6

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