On the Ideal Case of a Conjecture of Huneke and Wiegand

Olgur Celikbas, Shiro Goto, Ryo Takahashi, Naoki Taniguchi

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2 Citations (Scopus)

Abstract

A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free module with its algebraic dual always has torsion. Building on a beautiful result of Corso, Huneke, Katz and Vasconcelos, we prove that the conjecture is affirmative for a large class of ideals over arbitrary one-dimensional local domains. Furthermore, we study a higher-dimensional analogue of the conjecture for integrally closed ideals over Noetherian rings that are not necessarily local. We also consider a related question on the conjecture and give an affirmative answer for first syzygies of maximal Cohen-Macaulay modules.

Original languageEnglish
JournalProceedings of the Edinburgh Mathematical Society
DOIs
Publication statusPublished - 2019 Jan 1

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Keywords

  • integrally closed ideals
  • torsion in tensor products of modules
  • weakly m-full ideals

ASJC Scopus subject areas

  • Mathematics(all)

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