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

AbstractThe Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings k[Γ] can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup Γ. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where Γ is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences. [ABSTRACT FROM AUTHOR]