Every Finite Poset is Isomorphic to a Saturated Subset of the Spectrum of a Noetherian UFD

2022/06/06 by Colbert, Cory H., Loepp, S. · 2 citations
#13E05 #13F15 #13F40 (Primary) #13J10 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.02867

Abstract

We show that every finite poset is isomorphic to a saturated subset of the spectrum of a Noetherian unique factorization domain. In addition, we show that every finite poset is isomorphic to a saturated subset of the spectrum of a quasi-excellent domain.

Cited by

• Completions of Extremely Noncatenary Noetherian UFDs
• Dimension-Preserving Saturated Embeddings of Finite Posets into the Spectra of Noetherian UFDs

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