%0 Journal Article
%A Gamboa Mutuberria, José Manuel
%A Alonso García, María Emilia
%A Ruiz Pérez, Javier
%T Orderings On Real Surfaces
%D 1984
%@ 0764-4442
%U https://hdl.handle.net/20.500.14352/64631
%X 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 anirreducible 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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