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TitleGröbner bases applied to finitely generated field extensions
Author(s) Jörn Müller-Quade, Rainer Steinwandt
TypeArticle in Journal
AbstractUsing a constructive field-ideal correspondence it is shown how to compute the transcendence degree and a (separating) transcendence basis of finitely generated field extensionsk(x) / k(g), resp. how to determine the (separable)degree if k(x) / k(g) is algebraic. Moreover, this correspondence is used to derive a method for computing minimal polynomials and deciding field membership. Finally, a connection between certain intermediate fields of k(x) / k(g) and a minimal primary decomposition of a suitable ideal is described. For Galois extensions the field-ideal correspondence can also be used to determine the elements of the Galois group.
Length22
ISSN0747-7171
CopyrightAcademic Press
File
URL dx.doi.org/10.1006/jsco.1999.0417
LanguageEnglish
JournalJournal of Symbolic Computation
Volume30
Number4
Pages469-490
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year2000
MonthOctober
Translation No
Refereed No
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