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Título:
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On The Irreducible Components Of A Semialgebraic Set
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Autores:
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Gamboa, J. M. ;
Fernando Galván, José Francisco
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Tipo de documento:
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texto impreso
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Editorial:
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World Scientific Publ, 2012
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometria algebraica
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Tipo = Artículo
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Resumen:
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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.
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