Abstract
The Definition of the solution of an algebraic equation introduced in this note involves the explicite construction of the splitting-field and the exhibition of the roots in this field. It is shown in which cases a solution may be found by means of rational functions only. Furthermore a feasible solution-method is presented. This method is used to tackle other problems of Galois theory, too. As an example, the factorization of polynomials can be reduced to the determination of zeros of polynomials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Fröhlich, A., Shepherdson, J.C.: On the factorization of polynomials in a finite number of steps, Math. Z.62, 331–334 (1955)
Galois, E.: Mémoire sur les conditions de resolubilité des équations par radicaux, J. Math. pur. appl, Ser.1, vol. XI, 381–444 (1846)
Girstmair, K.: Konstruktive Galoistheorie, Dissertation, Innsbruck 1977
Girstmair, K., Oberst, U.: Ein Verfahren zur konstruktiven Bestimmung von Galoisgruppen, in: Jahrbuch Überblicke Mathematik 1976, Mannheim-Wien-Zürich: B.I. Wissenschaftsverlag
Haupt, O.: Einführung in die Algebra, Leipzig: Akademische Verlagsgesellschaft 1929
Serret, J.A.: Cours d'algèbre superieure, Paris: Gauthier-Villars 1885
Stauduhar, R.P.: The Determination of Galois Groups, Math. Comp.27, 981–996, (1973)
Zassenhaus, H.: On the group of an equation, in: Computers in Algebra and Number Theory, SIAM — AMS Proc. IV, 69–81 (1971)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Girstmair, K. Über konstruktive Methoden der Galoistheorie. Manuscripta Math 26, 423–441 (1979). https://doi.org/10.1007/BF01170265
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01170265