Date of Defense
1968
Department
Mathematics
First Advisor
John Petro, Mathematics
Abstract
The basic properties of topological groups are used to prove the Fundamental Theorem of Galois Theory for arbitrary extensions and present a discussion of topological groups followed by an investigation of infinite dimensional Galois theory. Classical Galois theory is concerned with the investigation of the group of G of permutations of the roots of a polynomial equation f(x) = 0 over the field of rational numbers Q. If K is the field obtained by adjoining the roots of this polynomial to Q, then K is a finite dimensional algebraic extension of Q, and G is the group of automorphisms of K that leave each element of Q fixed.
Recommended Citation
Sundstrom, Theodore A., "Topological Groups and Infinite Dimensional Galois Theory" (1968). Honors Theses. 305.
https://scholarworks.wmich.edu/honors_theses/305
Access Setting
Honors Thesis-Campus Only