Gamboa Mutuberria, José ManuelAlonso García, María EmiliaRuiz Pérez, Javier2023-06-212023-06-2119840764-4442https://hdl.handle.net/20.500.14352/64631After 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.journal articlemetadata only access512.71Álgebra1201 Álgebra