# Definition:Induced Homomorphism between Localizations of Ring

## Definition

Let $A$ be a commutative ring with unity.

Let $S, T \subseteq A$ be multiplicatively closed subsets.

Let $S$ be a subset of the saturation of $T$.

The induced homomorphism between localizations $A_S \to A_T$ is the unique $A$-algebra homomorphism between them.