Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 1

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

A prime ideal of $R$ is a proper ideal $P$ 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 Commutative and Unitary Ring