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Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture
- Publication Year :
- 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.
- Subjects :
- Mathematics - Commutative Algebra
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.12519
- Document Type :
- Working Paper