##  [Fractional Ideal](/fractional-ideal) 

  ##  [Fractional Ideal](https://puremath.quantumdictionary.io/fractional-ideal-0) 

  

 [![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

Given an integral domain R with field of fractions K, a fractional ideal is an R-submodule I of K for which there exists a nonzero r in R such that rI is an (integral) ideal of R. Fractional ideals allow denominators and extend ideal theory from R to K while retaining multiplicative structure.