##  [Krull–Schmidt Theorem](/krull-schmidt-theorem) 

  ##  [Krull–Schmidt Theorem](https://algebra.quantumdictionary.io/krull-schmidt-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 uniqueness result for direct-sum decompositions: under suitable finiteness hypotheses (for example modules of finite length or modules over a semiperfect ring), any decomposition of a module into indecomposable summands is unique up to ordering and isomorphism of the summands.