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$.