##  [Composition Series](/index.php/composition-series) 

  ##  [Composition Series](https://algebra.quantumdictionary.io/composition-series-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A finite chain of subobjects 0 = M_0 < M_1 < ... < M_n = M (for modules, groups, or similar algebraic structures) in which each successive quotient M_{i+1}/M_i is simple (has no nontrivial proper subobjects). The chain is used to decompose the object into irreducible building blocks called composition factors.