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

2019/01/09 by S. Loepp, Loepp, S., Alex Semendinger +1
Mathematics · Medicine · #13J10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Magnolia and Illicium research #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1901.02790

openalex publication_date 2019/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, given integers n₁,n₂, … ,n_k with 2 < n₁ < n₂ < ⋯ < n_k, there exists a local (Noetherian) unique factorization domain that has maximal chains of prime ideals of lengths n₁, n₂, … ,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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