 ##  [Maximal Ideal](/maximal-ideal) 

  ##  [Maximal Ideal](https://mathlogic.quantumdictionary.io/maximal-ideal-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 &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A proper ideal M of a ring R that is maximal with respect to inclusion among proper ideals; equivalently, the quotient ring R/M is a field.

 
 ##  [Maximal Ideal](https://algebra.quantumdictionary.io/maximal-ideal-1) 

  
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- Pure Mathematics -

**Algebra Dictionary**

 
Definition

A proper ideal M of a ring R that is maximal with respect to inclusion among proper ideals: there is no ideal I with M ⊊ I ⊊ R; equivalently R/M is a field.