Publication: Orderings On Real Surfaces
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Publication Date
1984
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Elsevier
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Abstract
After describing explicitly all total orderings in the ring R[[x, y]], we prove that each ordering in the quotient field of the ring of germs of real analytic functions at an
irreducible point O of a real analytic surface X is defined by a half-branch of the germ at O of some curve on X, which is analytic off the origin.
Then follows an analogous result for real algebraic surfaces.