##  [Adjoining an Element](/adjoining-element) 

  ##  [Adjoining an Element](https://algebra.quantumdictionary.io/adjoining-element-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 extending an algebraic structure by adding a new element (or symbols for elements) subject to specified algebraic relations, producing a larger object defined by generators and relations or by a universal property.