S. Phạm

A Counterexample to the Huneke-Wiegand Conjecture

We construct a symmetric numerical semigroup $\Gamma$ of multiplicity $56$, embedding dimension $26$, and Frobenius number $181$ such that, over every field $k$, the one-dimensional Gorenstein local domain $R=k[t^\Gamma]_{\mathfrak{m}}$ has a nonprincipal ideal $I=(t^{56},t^{70})R$ for which $I\otimes_R\operatorname{Ho...