Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 2

Definition
Let $\struct {R, +, \circ}$ be a commutative and unitary ring.

A prime ideal of $R$ is a proper ideal $P$ of $R$ such that:
 * $I \circ J \subseteq P \implies I \subseteq P \text { or } J \subseteq P$

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

Also see

 * Equivalence of Definitions of Prime Ideal of Commutative and Unitary Ring