Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584581 | Journal of Algebra | 2015 | 20 Pages |
Abstract
Let R be a Cohen–Macaulay local ring of dimension one with a canonical module KRKR. Let I be a faithful ideal of R . We explore the problem of when I⊗RI∨I⊗RI∨ is torsionfree, where I∨=HomR(I,KR)I∨=HomR(I,KR). We prove that if R has multiplicity at most 6, then I is isomorphic to R or KRKR as an R -module, once I⊗RI∨I⊗RI∨ is torsionfree. This result is applied to monomial ideals of numerical semigroup rings. A higher dimensional assertion is also discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shiro Goto, Ryo Takahashi, Naoki Taniguchi, Hoang Le Truong,