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Ordres sur les surfaces réelles Alonso García, María Emilia Gamboa Mutuberria, José Manuel Ruiz Sancho, Jesús María 512.7 Ordering in the quotient field of the ring of germs of real analytic functions real algebraic surfaces Geometria algebraica 1201.01 Geometría Algebraica 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. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-21T02:05:27Z 2023-06-21T02:05:27Z 1984 journal article https://hdl.handle.net/20.500.14352/64825 0764-4442 fra restricted access application/pdf Elsevier