Nash Functions - Local Properties

Local Properties

The local properties of Nash functions are well understood. The ring of 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 henselization of the ring of germs of rational functions. In particular, it is a regular local ring of dimension n.

Read more about this topic:  Nash Functions

Famous quotes containing the words local and/or properties:

    While it may not heighten our sympathy, wit widens our horizons by its flashes, revealing remote hidden affiliations and drawing laughter from far afield; humor, in contrast, strikes up fellow feeling, and though it does not leap so much across time and space, enriches our insight into the universal in familiar things, lending it a local habitation and a name.
    —Marie Collins Swabey. Comic Laughter, ch. 5, Yale University Press (1961)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)