# Definition:Antihomomorphism/Ring Antihomomorphism

Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.
Then $\phi: R \to S$ is a ring antihomomorphism if and only if:
$\forall a, b \in R: \map \phi {a + b} = \map \phi a \oplus \map \phi b$
$\forall a, b \in R: \map \phi {a \circ b} = \map \phi b * \map \phi a$