\begin{definition}[Definition:Initial Homomorphism from Integers to Ring with Unity]
Let $\Z$ be the ring of integers.
Let $R$ be a ring with unity.
The '''initial homomorphism''' $\Z \to R$ is the unital ring homomorphism that sends $n \in \Z$ to the $n$th power of $1$ in $R$:
:$ n \mapsto n \cdot 1$.
\end{definition}