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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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