##  [Hilbert Series](/hilbert-series) 

  ##  [Hilbert Series](https://algebra.quantumdictionary.io/hilbert-series-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The formal power series H(t)=Σ_{n∈Z} (dim or length of graded component in degree n) t^n that encodes the entire sequence of graded dimensions of a finitely generated graded module; often written as a rational function when the module is Noetherian.