Category:Prime Ideals of Rings

This category contains results about Prime Ideals of Rings.
Definitions specific to this category can be found in Definitions/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 $R$.

Also see

• Category:Prime Ideals (Order Theory)