Title

Galois Analysis of the Equation x5 - 2x3 - 3x2 + 6 = 0

Publication Year

1968

Keywords

equations, mathematics, Galois theory, algebra, splitting field, theorem

Disciplines

Algebra | Mathematics | Physical Sciences and Mathematics

Abstract

Galois theory is a description of the structure of field extensions. The main part of this work has been in applying the fundamental theorem of Galois theory to the extension of the rational numbers which is the splitting field for the polynomial x5 - 2x3 - 3x2 + 6 = 0. The full set of calculations for each splitting field has been included in the Appendix. This paper will attempt to develop the fundamental theorem and then show its application in the development of the splitting field of x5 - 2x3 - 3x2 + 6 = 0.

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