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]

PDF SchwartzTressl_ElPropZarSpec.pdf Download (447kB)

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:	https://eprints.maths.manchester.ac.uk/id/eprint/1157

Actions (login required)

View Item