Let R be a Cohen-Macaulay local ring of dimension one with a canonical module KR. Let I be a faithful ideal of R. We explore the problem of when I⊗RI∨ is torsionfree, where I∨=HomR(I, KR). We prove that if R has multiplicity at most 6, then I is isomorphic to R or KR as an R-module, once I⊗RI∨ is torsionfree. This result is applied to monomial ideals of numerical semigroup rings. A higher dimensional assertion is also discussed.
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