##  [Free Module](/free-module) 

  ##  [Free Module](https://algebra.quantumdictionary.io/free-module-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A module that admits a basis: it is isomorphic to a direct sum (possibly infinite) of copies of its coefficient ring R, with a distinguished set of elements (a basis) such that every element is a unique finite R-linear combination of basis elements.