Sur le theoreme de Stone-Weierstrass en Algebre commutative |
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Authors: | Jean-Luc Chabert |
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Affiliation: | 1. Institut Supérieur des Sciences et Techniques, Université de Picardie, 48, rue Raspail, 02109, St Quentin, France
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Abstract: | We show that the sufficient conditions given by Cahen, Grazzini and Haouat for a version of the Stone-Weierstrass theorem in commutative algebra are the widest. More precisely, letA be a Noetherian ring andI a proper ideal ofA such thatA is Hausdorff with respect to theI-adic topology. Note the completion ofA andC(Â,Â) the ring of continuous functions from to with uniform convergence topology. The subset of polynomial functions is dense inC(Â,Â) if and only if the radical ofI is a maximal idealm ofA and the local ringA m is a one-dimensional analytically irreducible domain with finite residue field. |
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