##  [Principal Ideal](/principal-ideal) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An ideal of a ring R generated by a single element a in R, denoted (a), consisting of all multiples r·a (or a·r) with r in R. Principal ideals are the simplest ideals and are central to the study of principal ideal domains and principal ideal behavior.