##  [Nakayama's Lemma](/nakayamas-lemma) 

  ##  [Nakayama's Lemma](https://algebra.quantumdictionary.io/nakayamas-lemma-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A statement about finitely generated modules over a local ring (or more generally over a ring with Jacobson radical J): if M is a finitely generated R-module and M = J M then M = 0; equivalently, a set of elements whose images generate M/JM lifts to generate M.