June 2023 A STRUCTURAL INVARIANT ON CERTAIN TWO-DIMENSIONAL NOETHERIAN PARTIALLY ORDERED SETS
Cory H. Colbert
Rocky Mountain J. Math. 53(3): 711-724 (June 2023). DOI: 10.1216/rmj.2023.53.711

Abstract

If (X,X) is a partially ordered set satisfying certain necessary conditions for X to be order-isomorphic to the spectrum of a Noetherian domain of dimension two, we describe a new poset (Str X,Str X) that completely determines X up to isomorphism. The order relation Str X imposed on Str X is modeled after R. Wiegand’s well-known “P5” condition that can be used to determine when a given partially ordered set (U,U) of a certain type is order-isomorphic to (Spec [x],).

Citation

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Cory H. Colbert. "A STRUCTURAL INVARIANT ON CERTAIN TWO-DIMENSIONAL NOETHERIAN PARTIALLY ORDERED SETS." Rocky Mountain J. Math. 53 (3) 711 - 724, June 2023. https://doi.org/10.1216/rmj.2023.53.711

Information

Received: 21 March 2022; Revised: 27 July 2022; Accepted: 19 August 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617907
zbMATH: 07731141
Digital Object Identifier: 10.1216/rmj.2023.53.711

Subjects:
Primary: 13E05

Keywords: Ascending chain condition , descending chain condition , invariant , Noetherian spectrum , ‎partially ordered set

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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