Elementary properties of minimal and maximal points in Zariski spectra |
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Authors: | Niels Schwartz Marcus Tressl |
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Institution: | 1. Universität Passau, FIM, D-94030 Passau, Germany;2. University of Manchester, School of Mathematics, Manchester M13 9PL, UK |
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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. |
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