\begin{definition}[Definition:Homomorphism (Abstract Algebra)/Image]
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:
:$\Img \phi = \set {t \in T: \exists s \in S: t = \map \phi s}$
\end{definition}