Definition:Ideal Quotient

Definition

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 $\mathfrak a$:

$\ideal {\mathfrak a : \mathfrak b} := \set {x \in A : x \mathfrak b \subseteq \mathfrak a}$

Also see

• Ideal Quotient is Ideal

Special cases

• Definition:Annihilator of Ideal of Ring