Difference between revisions of "Maximal ideal"
(New page: In ring theory, a '''maximal ideal''' of a ring <math>R</math> is a proper ideal <math>I\le R</math> which is not contained in any other proper ideal of <math>R</math>. (That i...) |
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Revision as of 00:43, 25 March 2009
In ring theory, a maximal ideal of a ring 
is a proper ideal 
which is not contained in any other proper ideal of . (That is, 
, and there is no ideal 
with 
.)
One important property of maximal ideals is that the quotient ring 
is a field iff 
is a maximal ideal of .
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