 ##  [Hensel Lifting](/hensel-lifting) 

  ##  [Hensel Lifting](https://mathlogic.quantumdictionary.io/hensel-lifting-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A procedure, based on Hensel's lemma, for lifting solutions of polynomial congruences or factorizations modulo a prime power p^k to solutions modulo higher powers p^{k+1}, often iterated to obtain p-adic solutions or factorizations in complete local rings.

 
 ##  [Hensel Lifting](https://puremath.quantumdictionary.io/hensel-lifting-1) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A method for lifting solutions of polynomial congruences modulo a prime power to solutions modulo higher powers (or to p-adic solutions), using local invertibility conditions often analogous to Newton iteration in the p-adic topology.