Alonso García, María EmiliaGamboa Mutuberria, José ManuelRuiz Sancho, Jesús María2023-06-212023-06-2119840764-4442https://hdl.handle.net/20.500.14352/64825After 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.frajournal articlehttp://gallica.bnf.fr/ark:/12148/bpt6k54939704/f43.image.r=Comptes%20Rendus%20de%20l%27Académie%20des%20Sciences.langENhttp://gallica.bnf.frrestricted access512.7Ordering in the quotient field of the ring of germs of real analytic functionsreal algebraic surfacesGeometria algebraica1201.01 Geometría Algebraica