##  [Base Change](/base-change) 

  ##  [Base Change](https://algebra.quantumdictionary.io/base-change-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 operation of transporting an algebraic object (module, algebra, sheaf, scheme, representation) along a homomorphism of base rings or base schemes f: R → S, typically realized by tensoring with S (S ⊗_R −) or by pullback along f; its effect is to reinterpret the object over the new base S.