Algebraic Closures

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: