Definition:Prime Ideal of Ring/Definition 1

Definition

Let $R$ be a ring.

A prime ideal of $R$ is an ideal $P$ of $R$ such that:

$\forall a, b \in R : a \circ b \in P \implies a \in P$ or $b \in P$

Also see

• Equivalence of Definitions of Prime Ideal of Ring

• Results about prime ideals of rings can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): prime ideal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prime ideal