References & Citations
Mathematics > Commutative Algebra
Title: Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture
(Submitted on 18 Apr 2024)
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.
Submission history
From: Christopher O'Neill [view email][v1] Thu, 18 Apr 2024 21:48:21 GMT (22kb,D)
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