# Definition:Initial Homomorphism from Integers to Ring with Unity

## Definition

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 $R$:

$n \mapsto n \cdot 1$.