Elementary properties of minimal and maximal points in Zariski spectra

Schwartz, Niels and Tressl, Marcus (2008) Elementary properties of minimal and maximal points in Zariski spectra. [MIMS Preprint]

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Abstract

We investigate connections between arithmetic properties of rings and topological properties of their prime spectrum. Any property that the prime spectrum of a ring may or may not have, defines the class of rings whose prime spectrum has the given property. We ask whether a class of rings defined in this way is axiomatizable in the model theoretic sense. Answers are provided for a variety of different properties of prime spectra, e.g., normality or complete normality, Hausdorffness of the space of maximal points, compactness of the space of minimal points.

Item Type: MIMS Preprint
Uncontrolled Keywords: commutative ring, prime ideal, spectral space, axiomatizability
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 08 General algebraic systems
MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
Depositing User: Dr Marcus Tressl
Date Deposited: 10 Oct 2008
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1157

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