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arXiv · 1901.02790

Maximal Chains of Prime Ideals of Different Lengths in Unique Factorization Domains

S. Loepp·Alex Semendinger
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Abstract

We show that, given integers $n_1,n_2, \ldots ,n_k$ with $2 < n_1 < n_2 < \cdots < n_k$, 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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S. Loepp, Alex Semendinger. 2019-01-09. Maximal Chains of Prime Ideals of Different Lengths in Unique Factorization Domains. https://arxiv.org/abs/1901.02790

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