On the Ideal Case of a Conjecture of Huneke and Wiegand. Issue 3 (11th February 2019)

• Record Type: Journal Article
• Authors: Celikbas, Olgur; Goto, Shiro; Takahashi, Ryo; Taniguchi, Naoki
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 3(2019)
• Page Start: 847
• Page End: 859
• Publication Date: 2019-02-11
• Subjects: integrally closed ideals, -- weakly m-full ideals, -- torsion in tensor products of modules; Primary 13D07, -- 13C14, -- 13C15; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091518000731
• Languages: English
• ISSNs: 0013-0915

Abstract

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.