An implicit function theorem for algebraically closed fields
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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 ClassificationPrimary: 12E12 Secondary: 08A40
Key words and phrasesalgebraically closed field algebraic function implicit equational definition
- 3.Campercholi, M., Vaggione, D.: Algebraic functions (2009, preprint)Google Scholar
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