Definition:Ordered Group Monomorphism

Definition

Let $\struct {S, \circ, \preceq}$ and $\struct {T, *, \preccurlyeq}$ be ordered groups.

An ordered group monomorphism from $\struct {S, \circ, \preceq}$ to $\struct {T, *, \preccurlyeq}$ is a mapping $\phi: S \to T$ that is both:

$(1): \quad$ A group monomorphism from the group $\struct {S, \circ}$ to the group $\struct {T, *}$

$(2): \quad$ An order embedding from the ordered set $\struct {S, \preceq}$ to the ordered set $\struct {T, \preccurlyeq}$.

Also see

• Definition:Ordered Structure Monomorphism

Linguistic Note

The word monomorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix mono- meaning single.

Thus monomorphism means single (similar) structure.