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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