Hilbert's Basis Theorem (Algebra 2: Lecture 12 Video 1)

Lecture 12: The focus of this lecture was on Hilbert's Basis Theorem: If R (a commutative ring with identity) is Noetherian, so is R[x]. We gave a full proof of this result and then gave a detailed sketch of a second proof. We mentioned some related facts, for example, if R is Noetherian, so is R[[x]]. At the end of the lecture we briefly talked about 'Ideal Membership' and motivation for Gröbner bases.