Category:Definitions/Prime Ideals of Rings

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This category contains definitions related to Prime Ideals of Rings.
Related results can be found in Category:Prime Ideals of Rings.

Let $R$ be a ring.

A prime ideal of $R$ is a proper ideal $P$ such that:

$I \circ J \subseteq P \implies I \subseteq P \text { or } J \subseteq P$

for any ideals $I$ and $J$ of $R$.