# Definition:Contraction of Ideal

## Definition

Let $A$ and $B$ be commutative ring with unity.

Let $f : A \to B$ be a ring homomorphism.

Let $\mathfrak b \subseteq B$ be an ideal.

The contraction of $\mathfrak b$ by $f$ is its preimage under $f$:

$\mathfrak b^c = f^{-1}(\mathfrak b)$