A local noetherian integral domain $A$ is a field if the unique maximal ideal $m$ satisfies $m^n = m^{n+1}$ for some $n\in N$
I think it should be related to Nakayama lemma, but cannot figure it out.
2026-05-04 14:54:08.1777906448
Prove that some local noetherian integral domain is a field
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Hint. Take $M=m^n$ in Nakayama's Lemma.