![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/previews/4ffeb29b-bc0a-4348-9d9f-512775d1bf2f.gif "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.
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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/previews/66c8fa09-83d3-4cb7-b038-9d3fd639fd3e_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.
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![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
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