This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their residue fields. We prove that all our cases are possible and give explicit constructions.
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Francisco Javier Herrera Govantes, Miguel Ángel Olalla Acosta, José Luis Vicente Córdoba, Valuations in fields of power series. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 467–482DOI 10.4171/RMI/358