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Fall and Winter 2016 Non-compact subsets of the Zariski space of an integral domain
Dario Spirito
Illinois J. Math. 60(3-4): 791-809 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067291

Abstract

Let $V$ be a minimal valuation overring of an integral domain $D$ and let $\operatorname{Zar}(D)$ be the Zariski space of the valuation overrings of $D$. Starting from a result in the theory of semistar operations, we prove a criterion under which the set $\operatorname{Zar}(D)\setminus\{V\}$ is not compact. We then use it to prove that, in many cases, $\operatorname{Zar}(D)$ is not a Noetherian space, and apply it to the study of the spaces of Kronecker function rings and of Noetherian overrings.

Citation

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Dario Spirito. "Non-compact subsets of the Zariski space of an integral domain." Illinois J. Math. 60 (3-4) 791 - 809, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067291

Information

Received: 19 September 2015; Revised: 3 May 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 06790327
MathSciNet: MR3705445
Digital Object Identifier: 10.1215/ijm/1506067291

Subjects:
Primary: 13F30
Secondary: 13A15, 13A18, 13B22, 54D30

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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