Dickson's lemma states that a monomial ideal has a finite basis. We give an explanation of the proof. This statement has a simple proof and can be used to prove the stronger Hilbert's basis theorem which states that every ideal in a polynomial ring has a finite basis.
0:00 Intro
0:23 Statement and consequences
2:14 Sketch of proof (n=2)
8:01 Sketch of proof (n=3)
== Relevant resources ==
Website for this lecture:
https://emresertoz.com/cag/
Book for this section:
Ideals, varieties, and algorithms by David Cox, Donal O'Shea, and John Little
== General description ==
This video is part of my "Computational Algebraic Geometry" lecture series taking place in Leibniz University Hannover (Germany).
Videos will be uploaded weekly on Monday and Wednesday afternoons during lecture times of the Winter Semester 2021/2022.
