Definition:Primary Ideal/Definition 1

Definition
Let $R$ be a commutative and unitary ring.

A priary ideal of $R$ is a proper ideal $\mathfrak q$ of $R$ such that:
 * $ x y \in \mathfrak q \implies x \in \mathfrak q \; \vee \; \exists n \in \Z_{>0} : y^n \in \mathfrak q$

Also see

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