Homomorphism

Given two magmas $A$ and $B$, a function $\phi : A \to B$ is a homomorphism if and only if $\phi(x \cdot y) = \phi(x) \cdot \phi(y)$, for all $x, y \in A$.

Remarks

A map between two algebraic structures that preserves that structure is, generally, called a homomorphism.