##  [Quotient Construction](/quotient-construction) 

  ##  [Quotient Construction](https://algebra.quantumdictionary.io/quotient-construction-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

The process of forming a new algebraic object by collapsing an original object along an equivalence relation (a congruence, ideal, normal subgroup, etc.) that is compatible with the operations, producing the quotient object whose elements are equivalence classes and whose operations are well-defined on those classes.