Let R be a commutative finite local ring which is not a field . Let be the maximal ideal of R . Can we conclude that ?
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Originally Posted by xixi Let R be a commutative finite local ring which is not a field . Let be the maximal ideal of R . Can we conclude that ? yes. is a finitely generated module. so, by Nakayama's lemma, if with the ideal then i.e. must be a field. contradiction!