Definition:Primary Ideal

Definition
Let $R$ be a commutative ring with unity.

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

is the radical of $\mathfrak q$ is the smallest prime ideal including $\mathfrak q$.

See Radical of Primary Ideal is Smallest Prime Ideal.

Also see

 * Equivalence of Definitions of Primary Ideal of Commutative Ring
 * Prime Ideal is Primary Ideal
 * Radical of Primary Ideal is Smallest Prime Ideal