##  [Variety (Universal Algebra)](/variety-universal-algebra) 

  ##  [Variety (Universal Algebra)](https://puremath.quantumdictionary.io/variety-universal-algebra-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variety in universal algebra is a class of algebras of the same signature closed under homomorphic images (H), subalgebras (S), and arbitrary direct products (P); equivalently, a class axiomatizable by a set of identities (equations).

 

 

 

 

 





 

 



 ##  [Variety (Universal Algebra)](https://algebra.quantumdictionary.io/variety-universal-algebra-1) 

  

 [![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 class of algebras of a fixed signature that is closed under homomorphic images, subalgebras, and arbitrary direct products; equivalently, the class of all models satisfying a given set of algebraic identities (equations).