Elementary properties of minimal and maximal points in Zariski spectra

JOURNAL OF ALGEBRA

卷:323

Article

Schwartz, Niels²  Tressl, Marcus¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Passau, FIM, D-94030 Passau, Germany

关键词: Commutative ring;    Prime ideal;    Spectral space;    Axiomatizability;   

DOI  :  10.1016/j.jalgebra.2009.11.003

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free