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:
“His farm was “grounds,” and not a farm at all;
His house among the local sheds and shanties
Rose like a factor’s at a trading station.”
—Robert Frost (1874–1963)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)