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Maximal ideal

Revision as of 23:43, 24 March 2009 by Jam (talk | contribs) (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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In ring theory, a maximal ideal of a ring $R$ is a proper ideal $I\le R$ which is not contained in any other proper ideal of $R$. (That is, $I\neq R$, and there is no ideal $J$ with $I<J<R$.)

One important property of maximal ideals is that the quotient ring $R/I$ is a field iff $I$ is a maximal ideal of $R$.

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