Universidad Complutense de Madrid
E-Prints Complutense

On Chains of prime ideals in ring of semialgebraic funtions

Impacto

Downloads

Downloads per month over past year

Fernando Galván, José Francisco (2014) On Chains of prime ideals in ring of semialgebraic funtions. Quaterly journal of mathematics, 65 (3). pp. 893-930. ISSN 0033-5606

[img] PDF
Restringido a Repository staff only

474kB

Official URL: http://qjmath.oxfordjournals.org/content/65/3/893.abstract



Abstract

In this work, we study the structure of non-refinable chains of prime ideals in the (real closed) rings S(M) and S*(M) of semialgebraic and bounded semialgebraic functions on a semialgebraic set M subset of R-m. We pay special attention to the prime z-ideals of S(M) and the minimal prime ideals of both rings. For the last, a decomposition of each semialgebraic set as an irredundant finite union of closed pure dimensional semialgebraic subsets plays a crucial role. We prove moreover the existence of maximal ideals in the ring S(M) of prefixed height whenever M is non-compact.


Item Type:Article
Uncontrolled Keywords:Semialgebraic function; Zariski spectrum; Maximal spectrum; Real closed ring; semialgebraic compactication; Chain of prime ideals; Maximal ideal; Minimal prime ideal; Z-ideal; Semialgebraic depth; Family of bricks; Local compactness
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:28164
Deposited On:10 Feb 2015 09:50
Last Modified:14 Jan 2016 18:08

Origin of downloads

Repository Staff Only: item control page