Finite Fields are Splitting Fields
Channel: Andrew Misseldine
Date: 2022-03-24

In this video, we prove that the order of a finite field is necessarily q=p^n, from some prime p. We prove that all finite fields are splitting fields for the polynomial x^q-x. Hence, all finite fields are determined by their order up to isomorphisms.

This is lecture 29 (part 2/2) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4230 - Abstract Algebra II at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: 
https://drive.google.com/file/d/1RiByZivi8dQkWJMlZP9yHtUpG0IwK5Y2/view

This lecture is based upon Sections 22.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.