On the Ideal Case of a Conjecture of Huneke and Wiegand
2019 ◽
Vol 62
(3)
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pp. 847-859
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AbstractA 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.
1997 ◽
Vol 27
(4)
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pp. 1065-1073
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1974 ◽
Vol 32
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pp. 330-331
1978 ◽
Vol 36
(1)
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pp. 100-101
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2016 ◽
Vol 30
(26)
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pp. 1650186
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2001 ◽
Vol 64
(1)
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pp. 71-79
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2007 ◽
Vol 208
(2)
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pp. 739-760
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2014 ◽
Vol 35
(7)
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pp. 2242-2268
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