# Definition:Initial Homomorphism from Integers to Ring with Unity

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## 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$.