Huneke-Wiegand conjecture and change of rings

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

doi:10.1016/j.jalgebra.2014.09.006

Huneke-Wiegand conjecture and change of rings

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Let R be a Cohen-Macaulay local ring of dimension one with a canonical module K_R. Let I be a faithful ideal of R. We explore the problem of when I⊗_RI^∨ is torsionfree, where I^∨=Hom_R(I, K_R). We prove that if R has multiplicity at most 6, then I is isomorphic to R or K_R 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 language	English
Pages (from-to)	33-52
Number of pages	20
Journal	Journal of Algebra
Volume	422
DOIs	https://doi.org/10.1016/j.jalgebra.2014.09.006
Publication status	Published - 2015 Jan 5
Externally published	Yes

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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10.1016/j.jalgebra.2014.09.006

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title = "Huneke-Wiegand conjecture and change of rings",

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.",

keywords = "Canonical module, Cohen-Macaulay ring, Gorenstein ring, Multiplicity, Numerical semigroup ring, Torsionfree",

author = "Shiro Goto and Ryo Takahashi and Naoki Taniguchi and {Le Truong}, Hoang",

year = "2015",

month = jan,

day = "5",

doi = "10.1016/j.jalgebra.2014.09.006",

language = "English",

volume = "422",

pages = "33--52",

journal = "Journal of Algebra",

issn = "0021-8693",

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T1 - Huneke-Wiegand conjecture and change of rings

AU - Goto, Shiro

AU - Takahashi, Ryo

AU - Taniguchi, Naoki

AU - Le Truong, Hoang

PY - 2015/1/5

Y1 - 2015/1/5

N2 - 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.

AB - 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.

KW - Canonical module

KW - Cohen-Macaulay ring

KW - Gorenstein ring

KW - Multiplicity

KW - Numerical semigroup ring

KW - Torsionfree

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U2 - 10.1016/j.jalgebra.2014.09.006

DO - 10.1016/j.jalgebra.2014.09.006

M3 - Article

AN - SCOPUS:84908587239

SN - 0021-8693

VL - 422

SP - 33

EP - 52

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Huneke-Wiegand conjecture and change of rings

Abstract

Keywords

ASJC Scopus subject areas

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