##  [Engel's Theorem](/engels-theorem) 

  ##  [Engel's Theorem](https://algebra.quantumdictionary.io/engels-theorem-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 theorem in Lie algebra theory stating that a finite-dimensional Lie algebra over a field for which every adjoint operator ad_x is nilpotent is itself a nilpotent Lie algebra.