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Título:
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On the nullstellensätze for stein spaces and C-analytic sets.
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Autores:
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Acquistapace, Francesca ;
Broglia, Fabrizio ;
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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American Mathematical Society, 2016
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Funciones (Matemáticas)
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Tipo = Artículo
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Resumen:
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In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ? Rn in terms of the saturation of ?ojasiewicz’s radical in O(X): The ideal I(?(a)) of the zero-set ?(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of ?ojasiewicz’s radical (Formula presented). If ?(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(?(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(?(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of ?(p).
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En línea:
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https://eprints.ucm.es/38181/1/Fernando108libre.pdf
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