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arXiv · 2404.12519

Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture

Miguel Landeros·Christopher O'Neill·Roberto Pelayo·Karina Peña·James Ren·Brian Wissman
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Abstract

The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. Garc\'ia-S\'anchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings $\Bbbk[\Gamma]$ can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup $\Gamma$. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where $\Gamma$ is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences.

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Miguel Landeros, Christopher O'Neill, Roberto Pelayo, Karina Peña, James Ren, Brian Wissman. 2024-04-18. Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture. https://arxiv.org/abs/2404.12519

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