Huneke-Wiegand conjecture and change of rings

Let $R$ be a Cohen-Macaulay local ring of dimension one with a canonical module ${\mathrm{K}}_{\mathrm{R}}$. Let $I$ be a faithful ideal of $R$. We explore the problem of when $I{\otimes }_R{I}^{\vee }$ is torsionfree, where $I^{\vee} = \operatorname{Hom_R(I, \rm{K_R})}$\mathrm{.}Weprovethatif$R$ has multiplicity at most $6$, then $I$ is isomorphic to $R$ or ${\mathrm{K}}_{\mathrm{R}}$ as an $R$-module, once $I{\otimes }_R{I}^{\vee }$ is torsionfree. This result is applied to monomial ideals of numerical semigroup rings. A higher dimensional assertion is also discussed.