Definition:Ideal Quotient of Commutative Ring

Definition
Let $R$ be a commutative ring.

Let $\mathfrak a, \mathfrak b$ be ideals of $R$.

The ideal quotient of $\mathfrak a$ and $\mathfrak b$ is the ideal defined as:
 * $\ds \ideal {\mathfrak a : \mathfrak b} := \set {x \in R : x \mathfrak b \subseteq \mathfrak a}$

where:
 * $x \mathfrak b := \set {x y : y \in \mathfrak b}$

Also see

 * Ideal Quotient is Ideal