Huneke-Wiegand conjecture and change of rings

Shiro Goto, Ryo Takahashi, Naoki Taniguchi, Hoang Le Truong

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)33-52
Number of pages20
JournalJournal of Algebra
Volume422
DOIs
Publication statusPublished - 2015 Jan 5
Externally publishedYes

Keywords

  • Canonical module
  • Cohen-Macaulay ring
  • Gorenstein ring
  • Multiplicity
  • Numerical semigroup ring
  • Torsionfree

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Goto, S., Takahashi, R., Taniguchi, N., & Le Truong, H. (2015). Huneke-Wiegand conjecture and change of rings. Journal of Algebra, 422, 33-52. https://doi.org/10.1016/j.jalgebra.2014.09.006