Algebraic Closures
Channel: Andrew Misseldine
Date: 2022-03-17

In this video, we define the notion of an algebraic closure of a field. We prove that every field has an algebraic closure and that they are unique up to isomorphism, by Zorn's Lemma. We do this by showing that an algebraic closure is a maximal algebraic extension.

This is lecture 27 (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/1SCe_3nIYET9XiSmJ_zQ-ZVB_qND-A3KG/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.