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Here is one exercise from some notes on graded rings. I tried but I got no idea to solve it. Please help me. Thanks.

Let $R$ be a graded ring. Prove that $R$ is Noetherian (Artinian) if and only if $R$ satisfies the ascending (descending) condition on homogeneous ideals.

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    What have you tried so far? The proof imitates the usual proof of the Hilbert Basis Theorem. This is already a direct hint to the solution ...2012-05-20
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    Can you post the solution? Sorry I am not good at algebra....2012-05-21

1 Answers 1