Category Theory and Galois Theory

Authors

Amanda Bower, University of Michigan--DearbornFollow

Abstract

Galois theory translates questions about fields into questions about groups. The fundamental theorem of Galois theory states that there is a bijection between the intermediate fields of a field extension and the subgroups of the corresponding Galois group. After a basic introduction to category and Galois theory, this project recasts the fundamental theorem of Galois theory using categorical language and illustrates this theorem and the structure it preserves through an example.

Author Bio

Amanda Bower is a graduating senior at the University of Michigan-Dearborn majoring in math and minoring in computer science and applied statistics. This paper is based on an independent study she did with Professor Thomas Fiore at the University of Michigan-Dearborn during Fall 2012. She is currently interested in algebraic topology and its applications and plans on applying to Ph.D. programs in math or computer science in the upcoming fall. She will be participating in the UCLA RIPS program in the summer of 2013.

Faculty Sponsor

Thomas Fiore

Recommended Citation

Bower, Amanda (2013) "Category Theory and Galois Theory," Rose-Hulman Undergraduate Mathematics Journal: Vol. 14: Iss. 1, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss1/10