# proof of Nakayama’s lemma

(This proof was taken from [1].)

If $M$ were not zero, it would have a simple quotient, isomorphic to $R/\U0001d52a$ for some maximal ideal^{} $\U0001d52a$ of $R$. Then we would have $\U0001d52aM\ne M$, so that $\U0001d51eM\ne M$ as $\U0001d51e\subseteq \U0001d52a$.

## References

- 1 Serre, J.-P. Local Algebra. Springer-Verlag, 2000.

Title | proof of Nakayama’s lemma |
---|---|

Canonical name | ProofOfNakayamasLemma |

Date of creation | 2013-03-22 13:16:50 |

Last modified on | 2013-03-22 13:16:50 |

Owner | nerdy2 (62) |

Last modified by | nerdy2 (62) |

Numerical id | 6 |

Author | nerdy2 (62) |

Entry type | Proof |

Classification | msc 13C99 |