Definition:Ordered Ring Automorphism
Jump to navigation
Jump to search
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
Linguistic Note
The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.
Thus automorphism means self structure.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $23$. The Field of Rational Numbers