Definition:Antihomomorphism/Ring Antihomomorphism
Jump to navigation
Jump to search
Definition
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.
Then $\phi: R \to S$ is a ring antihomomorphism if and only if:
\(\ds \forall a, b \in R: \, \) | \(\ds \map \phi {a + b}\) | \(=\) | \(\ds \map \phi a \oplus \map \phi b\) | |||||||||||
\(\ds \forall a, b \in R: \, \) | \(\ds \map \phi {a \circ b}\) | \(=\) | \(\ds \map \phi b * \map \phi a\) |