Huneke–Wiegand conjecture for two-generated ideals of symmetric numerical semigroup rings

Let $\Gamma$ be a symmetric numerical semigroup, let $\Bbbk$ be a field, and let $R=\Bbbk[\Gamma]$ be its semigroup algebra. Let $M$ be a 2-generated ideal of $R$, viewed as an $R$-module, and let $\operatorname{Hom}_R(M,R)$ denote its dual. Huneke–Wiegand conjecture. The torsion submodule of

$$M\otimes_R\operatorname{Hom}_R(M,R)$$

is non-trivial. This is a special case of the Huneke–Wiegand conjecture in commutative algebra. The paper states that this case is proved affirmatively for numerical semigroups generated by generalized arithmetic sequences, while the conjecture in general remains open.