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