##  [Conductor](/conductor) 

  ##  [Conductor](https://puremath.quantumdictionary.io/conductor-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

An ideal (or integer) that measures the failure of an order to be maximal or that records the extent of ramification and degeneration between two rings or of a representation; in number rings and orders it is the largest ideal contained in both the order and its integral closure.