Let $R$ be a ring. If $R[X]$ is noetherian, is R necessarily noetherian ?
I think that the answer is no, but could you show me the easiest example to understand ?
2026-03-28 22:26:27.1774736787
$R[X]$ noetherian with $R$ non noetherian
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Recall that if a commutative ring $A$ is Noetherian and $I$ is an ideal in $A$, then $A/I$ is also Noetherian. In this problem, take $A=R[X]$ and $I=(X)$.