Polynomial Rings are Euclidean Domains

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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:

Andrew Misseldine

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do we use strong induction? because degree of h(x) might not be n-1. So I guess we assume euclidian domain property holds for degrees 0, 1, .., n-1 and that implies n?

behzat

Why is the degree of g smaller then or equal to the degree of g + degree of q1-q2?

ibi

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