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![SOLVED: Prove the converse to Hilbert's Basis Theorem: if the polynomial ring R[x] is Noetherian, then R is Noetherian.](https://cdn.numerade.com/ask_previews/91bac205-6021-428e-9442-f5f7937ce172_large.jpg "SOLVED: Prove the converse to Hilbert's Basis Theorem: if the polynomial ring R[x] is Noetherian, then R is Noetherian.")
SOLVED: Prove the converse to Hilbert's Basis Theorem: if the polynomial ring R[x] is Noetherian, then R is Noetherian.
![abstract algebra - Clarifications on proof of Hilbert's Theorem for finitely generated graded modules over $k[x_1,...,x_r]$ - Mathematics Stack Exchange](https://i.stack.imgur.com/jfVPQ.png "abstract algebra - Clarifications on proof of Hilbert's Theorem for finitely generated graded modules over $k[x_1,...,x_r]$ - Mathematics Stack Exchange")
abstract algebra - Clarifications on proof of Hilbert's Theorem for finitely generated graded modules over $k[x_1,...,x_r]$ - Mathematics Stack Exchange
ORDINAL NUMBERS AND THE HILBERT BASIS THEOREM §1. Introduction. In [5] and [21] we studied countable algebra in the context of
arXiv:1401.4389v5 [math.RA] 22 Sep 2016
