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On The Irreducible Components Of A Semialgebraic Set

Gamboa Mutuberria, José Manuel and Fernando Galván, José Francisco (2012) On The Irreducible Components Of A Semialgebraic Set. International Journal Of Mathematics, 23 (4). p. 40. ISSN 0129-167X

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Abstract

In this work we define a semialgebraic set S Rn to be irreducible if the noetherian ring of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring : Substitution Theorem, Positivstellens¨atze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we
give full characterizations of the families of semialgebraic sets for which these classical results are true.


Item Type:Article
Uncontrolled Keywords:Nash function; Nash set; irreducible semialgebraic set; irreducible components of a semialgebraic set; w-Nash set; q-Nash set; substitution theorem; positivstellens ¨atze; 17th Hilbert problem and real nullstellensatz
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15390
Deposited On:28 May 2012 09:02
Last Modified:28 May 2012 09:02

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