![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 3. Let R be a commutative ring and let R[x] be the | Chegg.com](https://media.cheggcdn.com/media/509/509c998f-0556-468c-8e02-ae224982855a/php7JqNB8 "Solved 3. Let R be a commutative ring and let R[x] be the | Chegg.com")
Solved 3. Let R be a commutative ring and let R[x] be the | Chegg.com
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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
abstract algebra - Explanation of a proof from Stacks Project: Noetherian ring of formal powers series - Mathematics Stack Exchange
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PDF) A bottom-up approach to Hilbert's Basis Theorem
