\begin{definition}[Definition:Antihomomorphism/Ring Antihomomorphism]
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.
Then $\phi: R \to S$ is a '''ring antihomomorphism''' {{iff}}:
{{begin-eqn}}
{{eqn | q = \forall a, b \in R
      | l = \map \phi {a + b}
      | r = \map \phi a \oplus \map \phi b
}}
{{eqn | q = \forall a, b \in R
      | l = \map \phi {a \circ b}
      | r = \map \phi b * \map \phi a
}}
{{end-eqn}}
Category:Definitions/Antihomomorphisms
Category:Definitions/Ring Homomorphisms
\end{definition}