Definition:Prime Ideal of Ring/Commutative and Unitary Ring/Definition 3

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:
 * the complement $R \setminus P$ of $P$ in $R$ is closed under the ring product $\circ$.

Also see

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