On chains of prime ideals in rings of semialgebraic functions

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Fernando Galván, José Francisco (2014) On chains of prime ideals in rings of semialgebraic functions. Quarterly Journal of Mathematics, 65 (3). pp. 893-930. ISSN 0033-5606

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



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⊂ℝm. 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
Subjects:Sciences > Mathematics > Algebra
ID Code:29169
Deposited On:11 Mar 2015 09:25
Last Modified:22 Aug 2018 10:13

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