##  [Direct Product](/direct-product) 

  ##  [Direct Product](https://puremath.quantumdictionary.io/direct-product-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

The object whose elements are tuples with one coordinate from each factor and with componentwise operations, together with projection maps to each factor; categorically it is the product, representing families of maps into each factor.

 

 

 

 

 





 

 



 ##  [Direct Product](https://algebra.quantumdictionary.io/direct-product-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

The Cartesian product of a family of algebraic structures (modules, groups, rings) endowed with componentwise operations, consisting of all tuples with no finiteness restriction; it is the categorical product.