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A prime ideal $A$ of a commutative ring $R$ is a proper ideal of $R$ such that $a,b\in R$ and $ab\in A$ imply $a\in A$ or $b\in A$.
A maximal ideal $A$ of a commutative ring $R$ is a proper ideal of $R$ such that, whenever $B$ is an ideal of $R$ and $A\subseteq B\subseteq R$, then $B=A$ or $B=R$.

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Page last modified on January 21, 2014, at 09:24 AM

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HomePage Current Problems All Problems Pictures ProblemsByWeek List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Definition Prime Ideal And Maximal Ideal Please Login to access more options. Definition (Prime Ideal And Maximal Ideal) A prime ideal $A$ of a commutative ring $R$ is a proper ideal of $R$ such that $a,b\in R$ and $ab\in A$ imply $a\in A$ or $b\in A$. A maximal ideal $A$ of a commutative ring $R$ is a proper ideal of $R$ such that, whenever $B$ is an ideal of $R$ and $A\subseteq B\subseteq R$, then $B=A$ or $B=R$. The following pages link to this page. Definition.PrimeIdealAndMaximalIdeal Schedule.20140117 Schedule.20140124 Schedule.20140127 Schedule.20170125 Schedule.20170127 Schedule.20170130 Schedule.AllProblems442 Edit Page History Source Attach File Backlinks List Group Page last modified on January 21, 2014, at 09:24 AM
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