##  [Zero Product Property](/zero-product-property) 

  ##  [Zero Product Property](https://algebra.quantumdictionary.io/zero-product-property-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 principle that, in certain algebraic structures with an absorbing zero element, a product equals zero only if at least one of the factors equals zero; typically expressed as: if a·b = 0 then a = 0 or b = 0, when the property holds.