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Recognizing Simple Subextensions of Purely Transcendental Field Extensions

  • Jörn Müller-Quade
  • Rainer Steinwandt

Abstract.

Let k(X)/k be a finitely generated purely transcendental extension of fields with transcendence basis X. From a generalization of Lüroth's theorem it is known that all intermediate fields K of k(X)/k with (K/k) = 1 are of the form K = k(f) for some fk(X). In this note we give a criterion which allows to decide effectively whether the extension K/k is simple if a finite generating set of K over k is known and computations in K are effective. In the affirmative case a primitive element of K over k is computed.

Keywords: Rational function fields, Primitive element, Gröbner bases. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jörn Müller-Quade
    • 1
  • Rainer Steinwandt
    • 1
  1. 1.Institut für Algorithmen und Kognitive Systeme, Professor Dr. Th. Beth, Arbeitsgruppe Computeralgebra, Fakultät für Informatik, Universität Karlsruhe, 76131-Karlsruhe, GermanyDE

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