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On Lojasiewicz's inequality and the Nullstellensatz for rings of semialgebraic functions

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Fernando Galván, José Francisco and Gamboa, J. M. (2014) On Lojasiewicz's inequality and the Nullstellensatz for rings of semialgebraic functions. Journal of algebra, 399 . pp. 475-488. ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021869313005991




Abstract

In this article we present versions of Lojasiewicz's inequality and the Nullstellensatz for the ring of bounded semialgebraic functions on an arbitrary semialgebraic set M. We also prove that the classical Lojasiewicz inequality and Nullstellensatz for the ring of semialgebraic functions on a semialgebraic set M work if and only if M is locally compact.


Item Type:Article
Uncontrolled Keywords:Semialgebraic set; Semialgebraic function; Lojasiewicz's inequality; Nullstellensatze; Locally compact semialgebraic set; z-ideal; z*-ideal; Radical ideal; Prime ideal; Maximal ideal; Fixed ideal; Free ideal
Subjects:Sciences > Mathematics > Algebra
ID Code:24697
Deposited On:17 Mar 2014 11:17
Last Modified:02 Mar 2016 14:22

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