Abstract
We provide an expression for the conductor \(c(\varDelta )\) of a semimodule \(\varDelta \) of a numerical semigroup \(\varGamma \) with two generators in terms of the syzygy module of \(\varDelta \) and the generators of the semigroup. In particular, we deduce that the difference between the conductor of the semimodule and the conductor of the semigroup is an element of \(\varGamma \), as well as a formula for \(c(\varDelta )\) in terms of the dual semimodule of \(\varDelta \).
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Communicated by Jorge Almeida.
Dedicated to the memory of Fernando Eduardo Torres Orihuela
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The first named author was partially supported by Spanish Goverment, Ministerios de Ciencia e Innovación y de Universidades MTM2016-76868-C2-1-P. The second named author was partially supported by the Spanish Government, Ministerios de Ciencia e Innovación y de Universidades, grant PGC2018-096446-B-C22, as well as by Universitat Jaume I, grant UJI-B2018-10.
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Almirón, P., Moyano-Fernández, J.J. A formula for the conductor of a semimodule of a numerical semigroup with two generators. Semigroup Forum 103, 278–285 (2021). https://doi.org/10.1007/s00233-021-10182-1
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DOI: https://doi.org/10.1007/s00233-021-10182-1