Abstract
We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers. Moreover, we give a way to construct all the almost symmetric semigroups with embedding dimension four and type three generated by odd elements. In this case we also prove that all the pseudo-Frobenius numbers are multiple of one of them and this gives many consequences on the semigroup and its defining ideal.
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Acknowledgements
This work began when the second author was visiting the University of Catania and he would like to express his hearty thanks for the hospitality of Marco D’Anna. The first author was supported by INdAM, more precisely he was “titolare di una borsa per l’estero dell’Istituto Nazionale di Alta Matematica”.
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Strazzanti, F., Watanabe, Ki. (2020). Almost Symmetric Numerical Semigroups with Odd Generators. In: Barucci, V., Chapman, S., D'Anna, M., Fröberg, R. (eds) Numerical Semigroups . Springer INdAM Series, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-030-40822-0_19
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DOI: https://doi.org/10.1007/978-3-030-40822-0_19
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