\begin{definition}[Definition:Contraction of Ideal]
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 $f$:
:$\mathfrak b^c = f^{-1}(\mathfrak b)$
\end{definition}