On the Ideal Case of a Conjecture of Huneke and Wiegand

Olgur Celikbas, Shiro Goto, Ryo Takahashi, Naoki Taniguchi*

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ジャーナルProceedings of the Edinburgh Mathematical Society
DOI
出版ステータスPublished - 2019 1月 1

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「On the Ideal Case of a Conjecture of Huneke and Wiegand」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル