Huneke-Wiegand conjecture and change of rings

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

Research output: Contribution to journalArticle

5 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

Fingerprint

Canonical Module
Numerical Semigroup
Semigroup Ring
Cohen-Macaulay Ring
Monomial Ideals
Local Ring
Faithful
Assertion
One Dimension
Multiplicity
High-dimensional
Isomorphic
Ring
Module

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Huneke-Wiegand conjecture and change of rings. / Goto, Shiro; Takahashi, Ryo; Taniguchi, Naoki; Le Truong, Hoang.

In: Journal of Algebra, Vol. 422, 05.01.2015, p. 33-52.

Research output: Contribution to journalArticle

Goto, Shiro ; Takahashi, Ryo ; Taniguchi, Naoki ; Le Truong, Hoang. / Huneke-Wiegand conjecture and change of rings. In: Journal of Algebra. 2015 ; Vol. 422. pp. 33-52.
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