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Título:
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Separation, factorization and finite sheaves on Nash manifolds
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Autores:
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Coste, M. ;
Ruiz Sancho, Jesús María ;
Shiota, Masahiro
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Tipo de documento:
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texto impreso
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Editorial:
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Cambridge University Press, 1996-08
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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/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: Geometria algebraica
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Materia = Ciencias: Matemáticas: Teoría de conjuntos
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Materia = Ciencias: Matemáticas: Topología
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Tipo = Artículo
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Resumen:
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Nash functions are those real analytic functions which are algebraic over the polynomials. Let M?Rn be a Nash manifold, N(M) the ring of Nash functions on M and O(M) the ring of analytic functions on M. The following problems have been open for at least twenty years: (1) Separation problem: Let G be a prime ideal of N(M); is G?O(M) a prime ideal? (2) Factorisation problem: Given f?N(M) and an analytic factorisation f=f1?f2, do there exist Nash functions g1,g2 on M and positive analytic functions ?1,?2 such that ?1??2=1 and f1=?1g1, f2=?2g2? (3) Global equations problem: Is every finite sheaf I of ideals of N generated by global Nash functions? (4) Extension problem: For the same I as above, is the natural homomorphism H0(M,N)?H0(M,N/I) surjective? The main results of this paper are: Theorem. For any Nash manifold M, Problem 1 has a positive answer if and only if Problem 3 (or Problem 4) have a positive answer. Problem 3 has a positive answer for any locally principal finite sheaf if and only if Problem 2 has a positive answer. It is interesting to remark that the authors, in a recent paper, have proved that the above problems have a positive answer under the hypothesis that M be compact.
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En línea:
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https://eprints.ucm.es/id/eprint/20011/1/RuizSancho11.pdf
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