Definition:Ordered Ring Automorphism

Definition
Let $\left({R, +, \circ, \preceq}\right)$ be an ordered ring.

An ordered ring automorphism from $\left({R, +, \circ, \preceq}\right)$ to itself is a mapping $\phi: R \to R$ that is both:


 * An ordered group automorphism from the ordered group $\left({R, +, \preceq}\right)$ to itself


 * A semigroup automorphism from the semigroup $\left({R, \circ}\right)$ to itself.

Also see

 * Ordered Structure Automorphism