##  [Hensel's Lemma](/hensels-lemma) 

  ##  [Hensel's Lemma](https://algebra.quantumdictionary.io/hensels-lemma-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 lifting principle in p-adic and modular arithmetic that, under suitable derivative (nondegeneracy) conditions, allows a solution of a polynomial congruence modulo p^n to be lifted to a solution modulo higher powers p^{n+k}, ultimately giving a root in the p-adic integers.