Definition:Homomorphism (Abstract Algebra)/Image

Definition
Let $S$ and $T$ be algebraic structures.

Let $\phi: S \to T$ be a homomorphism from $S$ to $T$.

As a homomorphism is a mapping, the homomorphic image of $\phi$ is defined in the same way as the image of a mapping:


 * $\operatorname{Im} \left({\phi}\right) = \left\{{t \in T: \exists s \in S: t = \phi \left({s}\right)}\right\}$