Definition:Ordered Group Monomorphism

Definition
Let $\left({S, \circ, \preceq}\right)$ and $\left({T, *, \preccurlyeq}\right)$ be ordered groups.

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


 * A group monomorphism from the group $\left({S, \circ}\right)$ to the group $\left({T, *}\right)$


 * An order embedding from the poset $\left({S, \preceq}\right)$ to the poset $\left({T, \preccurlyeq}\right)$.

Also see

 * Definition:Ordered Structure Monomorphism