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TakuyaMurata (talk | contribs) m TakuyaMurata moved page Nash functions to Nash function over redirect: Prefer singular to plural |
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==Local properties==
The local properties of Nash functions are well understood. The ring of [[germ (mathematics)|germs]] of Nash functions at a point of a Nash manifold of dimension ''n'' is isomorphic to the ring of algebraic [[power series]] in ''n'' variables (i.e., those series satisfying a nontrivial polynomial equation), which is the [[hensel's lemma|henselization]] of the ring of germs of rational functions. In particular, it is a [[regular local ring]] of dimension ''n''.
==Global properties==
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#J. Bochnak, M. Coste and M-F. Roy: Real algebraic geometry. Springer, 1998.
#M. Coste, J.M. Ruiz and M. Shiota: Global problems on Nash functions. Revista
#G. Efroymson: A Nullstellensatz for Nash rings. Pacific J. Math. 54 (1974), 101--112.
#J.F. Nash : Real algebraic manifolds. Annals of Mathematics 56 (1952), 405--421.
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