Algebra universalis

, 65:299 | Cite as

An implicit function theorem for algebraically closed fields

Article

Abstract

Let F be an algebraically closed field of characteristic 0, and let f : F n F. We show that f is implicitly definable by a system of polynomial equations if and only if f is a special kind of piecewise rational function.

2010 Mathematics Subject Classification

Primary: 12E12 Secondary: 08A40 

Key words and phrases

algebraically closed field algebraic function implicit equational definition 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Facultad de Matemática, Astronomía y FísicaUniversidad Nacional de CórdobaCórdobaArgentina

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