##  [Hilbert–Samuel Multiplicity](/hilbert-samuel-multiplicity) 

  ##  [Hilbert–Samuel Multiplicity](https://algebra.quantumdictionary.io/hilbert-samuel-multiplicity-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A numerical invariant e(I,M) defined for an m-primary ideal I in a Noetherian local ring (A,m) and a finitely generated A-module M that measures the leading-term growth of the length of M/I^nM as a polynomial in n for large n; equivalently the normalized leading coefficient of the Hilbert–Samuel polynomial.