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On Chains of prime ideals in ring of semialgebraic funtions



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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

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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 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

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