# Category:Definitions/Prime Ideals of Rings

Jump to navigation
Jump to search

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 $R$.

## Pages in category "Definitions/Prime Ideals of Rings"

The following 5 pages are in this category, out of 5 total.

### P

- Definition:Prime Ideal of Commutative and Unitary Ring
- Definition:Prime Ideal of Ring
- Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 1
- Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 2
- Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 3