Galois Analysis of the Equation x5 - 2x3 - 3x2 + 6 = 0
equations, mathematics, Galois theory, algebra, splitting field, theorem
Algebra | Mathematics | Physical Sciences and Mathematics
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.
Spiess, K. W. (1968). Galois Analysis of the Equation x5 - 2x3 - 3x2 + 6 = 0 (Undergraduate honors thesis, University of Redlands). Retrieved from https://inspire.redlands.edu/cas_honors/809