##  [Adjoining a Unit](/adjoining-unit) 

  ##  [Adjoining a Unit](https://algebra.quantumdictionary.io/adjoining-unit-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 construction that embeds a nonunital algebraic structure (ring, algebra, or similar) into a unital one by formally adjoining a multiplicative identity element and extending the operations so that the new element acts as an identity.