feat(ring_theory/noetherian): Nakayama's Lemma #778
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jcommelin
reviewed
Mar 1, 2019
jcommelin
reviewed
Mar 1, 2019
| /-- Nakayama's Lemma. Atiyah-Macdonald 2.5, Eisenbud 4.7, Matsumura 2.2, Stacks 10.19.1 (00DV) -/ | ||
| theorem exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul {R : Type*} [comm_ring R] | ||
| {M : Type*} [add_comm_group M] [module R M] | ||
| (I : ideal R) (N : submodule R M) (hn : N.fg) (hin : N ≤ I • N) : |
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Can you also give the corollary for finitely generated modules. (I.e., the version that does not mention submodules.) I guess that is a statement that will be applied quite often.
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How would you state it?
Co-Authored-By: kckennylau <kc_kennylau@yahoo.com.hk>
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