Let $R$ be a noetherian ring and let $R[x_1, \dots, x_n]$ be the polynomial ring in $n$ variables over $R$. Is it true that $\mathfrak{m}=(x_1, \dots, x_n)$ is a maximal ideal in $R[x_1, \dots, x_n]$? If not, then what are the maximal ideals? Thanks.
2026-03-30 07:11:29.1774854689
Maximal ideals in a polynomial ring over a noetherian ring.
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