Publication: Ordres sur les surfaces réelles
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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.
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G. W. BRUMFIEL, Partially ordered rings and semi-algebraic geometry (Lecture Notes, 37, Cambridge University Press, 1978)
L. Fuchs, Partially ordered algebraic systems, Pergamon Press, 1963
R. Narasimhan, Introduction to the theory of analytic spaces (Lecture Notes, 25, Springer, 1966)
R. J. Walker, Algebraic curves, Princeton University Press, 1950