Definition:Antihomomorphism/Ring Antihomomorphism

Definition
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.

Then $\phi: R \to S$ is a ring antihomomorphism :
 * $\forall a, b \in R: \map \phi {a + b} = \map \phi a \oplus \map \phi b$
 * $\forall a, b \in R: \map \phi {a \circ b} = \map \phi b * \map \phi a$