Definition:Primary Ideal

Definition
Let $R$ be a commutative ring.

also Known as
A primary ideal $\mathfrak q$ is also called $\mathfrak p$-primary, where
 * $\mathfrak p := \map \Rad {\mathfrak q}$

is the smallest prime ideal including $\mathfrak q$, see Radical of Primary Ideal.

Also see

 * Equivalence of Definitions of Primary Ideal of Commutative Ring
 * Radical of Primary Ideal