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2019 Maximal chains of prime ideals of different lengths in unique factorization domains
Susan Loepp, Alex Semendinger
Rocky Mountain J. Math. 49(3): 849-865 (2019). DOI: 10.1216/RMJ-2019-49-3-849

Abstract

We show that, given integers $n_1,n_2, \ldots ,n_k$ with $2 \lt n_1 \lt n_2 \lt \cdots \lt n_k$, there exists a local (Noetherian) unique factorization domain that has maximal chains of prime ideals of lengths $n_1, n_2, \ldots ,n_k$ which are disjoint except at their minimal and maximal elements. In addition, we demonstrate that unique factorization domains can have other unusual prime ideal structures.

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Susan Loepp. Alex Semendinger. "Maximal chains of prime ideals of different lengths in unique factorization domains." Rocky Mountain J. Math. 49 (3) 849 - 865, 2019. https://doi.org/10.1216/RMJ-2019-49-3-849

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088339
MathSciNet: MR3983303
Digital Object Identifier: 10.1216/RMJ-2019-49-3-849

Subjects:
Primary: 13C15

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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