##  [Localization](/localization) 

  ##  [Localization](https://mathlogic.quantumdictionary.io/localization-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The process of inverting a specified multiplicative set S in a ring or analogous elements in other algebraic structures to form a new object S^{-1}R in which elements of S become units; more generally, formally adjoining inverses along a chosen class of morphisms in a category.

 

 

 

 

 





 

 



 ##  [Localization](https://puremath.quantumdictionary.io/localization-1) 

  

 [![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 construction of a new object by formally adjoining inverses to a specified multiplicative subset, thereby inverting chosen elements while preserving the rest of the structure via a universal property.

 

 

 

 

 





 

 



 ##  [Localization](https://algebra.quantumdictionary.io/localization-2) 

  

 [![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 process of adjoining inverses to a chosen multiplicative subset S of an algebraic object (typically a ring or monoid) to form a localized object S^{-1}A in which every element of S becomes invertible; equivalently, the universal construction that makes specified elements units while preserving as much of the original structure as possible.