##  [Nilpotency Index](/nilpotency-index) 

  ##  [Nilpotency Index](https://puremath.quantumdictionary.io/nilpotency-index-0) 

  

 [![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 & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The smallest positive integer n such that x^n=0 for a nilpotent element x in a ring or algebra; equivalently the length of the longest nontrivial power chain before the element annihilates.