\begin{definition}[Definition:Ideal Quotient]
Let $A$ be a commutative ring with unity.
Let $\mathfrak a, \mathfrak b \subseteq A$ be ideals of $A$.
Their '''ideal quotient''' is the ideal consisting of elements whose product with $\mathfrak b$ is a subset of $\mathfrak a$:
:$\ideal {\mathfrak a : \mathfrak b} := \set {x \in A : x \mathfrak b \subseteq \mathfrak a}$
\end{definition}