##  [Artin Approximation](/artin-approximation) 

  ##  [Artin Approximation](https://algebra.quantumdictionary.io/artin-approximation-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

A technique and theorem that produces algebraic or convergent approximations to formal power-series solutions of polynomial systems, asserting that a formal solution can be approximated to any finite order by algebraic or convergent solutions under suitable hypotheses.