##  [Flatness](/flatness) 

  ##  [Flatness](https://algebra.quantumdictionary.io/flatness-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 property of a module M over a ring R (or of a ring homomorphism R → S) meaning that tensoring with M (or with S over R) preserves exact sequences; equivalently Tor1^R(−,M) = 0 for all modules, so no new torsion is introduced by tensor product.