Definition:Ordered Ring Automorphism

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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.


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