Examples of Euclidean Domains I (Algebra 2: Lecture 3 Video 3)

Lecture 3: We started this lecture with a description of the overall topic of Chapter 8. We then showed that Z is a principal ideal domain (which we already knew), and also that when F is a field F[x] is a PID. We defined a Euclidean domain and said a little about the Euclidean algorithm in Z. We then discussed the Euclidean algorithm in a general Euclidean domain, which we will say more about in the next lecture. We gave several examples of Euclidean domains including fields, Z, F[x] for a field F, and Z[i]. We then proved that a Euclidean domain is a PID. This gave a way to show that an integral domain is not a Euclidean domain. We showed an example of this kind of argument.