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arXiv · 2311.15265

The isomorphism problem for ideal class monoids of numerical semigroups

Pedro A. Garcia-Sanchez
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Abstract

From any poset isomorphic to the poset of gaps of a numerical semigroup $S$ with the order induced by $S$, one can recover $S$. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups $S$ and $T$, if their ideal class monoids are isomorphic, then $S$ must be equal to $T$.

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Pedro A. Garcia-Sanchez. 2024-04-05. The isomorphism problem for ideal class monoids of numerical semigroups. https://arxiv.org/abs/2311.15265

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