##  [Double Centralizer Theorem](/double-centralizer-theorem) 

  ##  [Double Centralizer Theorem](https://algebra.quantumdictionary.io/double-centralizer-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 structural result identifying an algebra with the centralizer of its centralizer when an algebra A acts faithfully on a module M under suitable finiteness or semisimplicity hypotheses: under these conditions A ≅ End_{End_A(M)}(M), i.e., taking the centralizer twice recovers the original acting algebra.