Definition:Isomorphism (Abstract Algebra)/Ordered Structure Isomorphism

Definition
An ordered structure isomorphism from an ordered structure $\struct {S, \circ, \preceq}$ to another $\struct {T, *, \preccurlyeq}$ is a mapping $\phi: S \to T$ that is both:


 * $(1): \quad$ An isomorphism, that is a bijective homomorphism, from the structure $\struct {S, \circ}$ to the structure $\struct {T, *}$
 * $(2): \quad$ An order isomorphism from the ordered set $\struct {S, \preceq}$ to the ordered set $\struct {T, \preccurlyeq}$.

Also see

 * Definition:Isomorphism (Abstract Algebra)
 * Definition:Order Isomorphism