Polynomial Rings are Euclidean Domains
Channel: Andrew Misseldine
Date: 2022-02-11

In this video, we prove that a polynomial ring whose coefficient ring is a field has a Euclidean norm and hence is a Euclidean domain. Specifically, a division algorithm is available on these polynomial rings.

This is lecture 19 (part 4/4) 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/1Tan6ysJN1cjn_V-MkyMma9sfDbHpcBgC/view

This lecture is based upon Section 17.1 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.