from Wikipedia
« »  
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
In a principal ideal domain every nonzero prime ideal is maximal, but this is not true in general.

1.815 seconds.