![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.](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.
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Master of Science (Mathematics) Second Semester Examination, June-2021 Advanced Abstract Algebra-II [MSM201T] Time: 3:00 Hrs
![abstract algebra - Explanation of a proof from Stacks Project: Noetherian ring of formal powers series - Mathematics Stack Exchange abstract algebra - Explanation of a proof from Stacks Project: Noetherian ring of formal powers series - Mathematics Stack Exchange](https://i.stack.imgur.com/9DC25.png)