Definition:Ideal Quotient
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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 $\mathfrak a$:
- $\ideal {\mathfrak a : \mathfrak b} := \set {x \in A : x \mathfrak b \subseteq \mathfrak a}$
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