Definition:Ordered Ring Automorphism

Definition
Let $\struct {R, +, \circ, \preceq}$ be an ordered ring.

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


 * $(1): \quad$ An ordered group automorphism from the ordered group $\struct {R, +, \preceq}$ to itself


 * $(2): \quad$ A semigroup automorphism from the semigroup $\struct {R, \circ}$ to itself.

Also see

 * Definition:Ordered Structure Automorphism