\begin{definition}[Definition:Induced Mapping on Spectra of Rings]
Let $A$ and $B$ be commutative rings with unity.
Let $f : A \to B$ be a ring homomorphism.
The '''induced mapping on spectra by $f$''' is the mapping $f^* : \Spec B \to \Spec A$ between their spectra with:
:$\map {f^*} {\mathfrak p} = \map {f^{-1} } {\mathfrak p}$,
the preimage of a prime ideal $\mathfrak p \in \Spec B$.
\end{definition}