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2008.85: Elementary properties of minimal and maximal points in Zariski spectra

2008.85: Niels Schwartz and Marcus Tressl (2008) Elementary properties of minimal and maximal points in Zariski spectra.

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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 2000 > 08 General algebraic systems
MSC 2000 > 14 Algebraic geometry
MIMS number:2008.85
Deposited By:Dr Marcus Tressl
Deposited On:10 October 2008

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