Degrees of a Field Extension
Channel: Andrew Misseldine
Date: 2022-03-17

In this video, we prove the analog of Lagrange's Theorem of field degrees, that is, the degree of the extension K/F factors over the degrees of the intermediate field E, that is, [K : F] = [K : E][E : F]. We explore some examples and consequences of this result.

This is lecture 26 (part 3/3) 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/1SKDRvo-eeGuhhI0VBlWEptLlnKn7BSr4/view

This lecture is based upon Sections 21.1 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.