##  [Peirce Decomposition](/peirce-decomposition) 

  ##  [Peirce Decomposition](https://algebra.quantumdictionary.io/peirce-decomposition-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 canonical splitting of an associative algebra A determined by an idempotent e (e^2 = e) that writes A as a direct sum of four natural bimodule components: eAe, eA(1−e), (1−e)Ae, and (1−e)A(1−e). It organizes elements by how left and right multiplication by e project them into block-like subspaces.