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Simplicial Affine Semigroups with Monomial Minimal Reduction Ideals

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Abstract

We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen–Macaulay and Gorenstein properties of the associated graded ring and provide several bounds for the reduction number with respect to the monomial minimal reduction.

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Acknowledgements

The first author was partially funded by the project “Proprietà locali e globali di anelli e di varietà algebriche”-PIACERI 2020–2022 Università degli Studi di Catania. The second author acknowledges the receipt of a grant from the ICTP-INdAM Research in Pairs Programme, Trieste, Italy. She was in part supported by a grant from IPM (no. 1400130112). The third author was partially supported by INdAM, more precisely he was “titolare di un Assegno di Ricerca dell’Istituto Nazionale di Alta Matematica”. Part of this work has been developed during the visit of the second author to the Department of Mathematics and Computer Science, University of Catania in 2019. The authors would like to thank the Department for its hospitality and support. The authors would also like to thank the anonymous referee for her/his careful reading of this paper and for many remarks that helped them to improve its quality. Funding was provided by Institute for Research in Fundamental Sciences.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6, 95125, Catania, Italy

    Marco D’Anna

  2. Mosaheb Institute of Mathematics, Kharazmi University, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Raheleh Jafari

  3. Dipartimento di Matematica, Università degli Studi di Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    Francesco Strazzanti

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  1. Marco D’Anna
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  2. Raheleh Jafari
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  3. Francesco Strazzanti
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Correspondence to Raheleh Jafari.

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D’Anna, M., Jafari, R. & Strazzanti, F. Simplicial Affine Semigroups with Monomial Minimal Reduction Ideals. Mediterr. J. Math. 19, 84 (2022). https://doi.org/10.1007/s00009-022-02003-8

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  • DOI: https://doi.org/10.1007/s00009-022-02003-8

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