Definition:Ordered Ring Monomorphism

Definition
Let $\struct {S, +, \circ, \preceq}$ and $\struct {T, \oplus, *, \preccurlyeq}$ be ordered rings.

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


 * $(1): \quad$ An ordered group monomorphism from the ordered group $\struct {S, +, \preceq}$ to the ordered group $\struct {T, \oplus, \preccurlyeq}$


 * $(2): \quad$ A semigroup monomorphism from the semigroup $\struct {S, \circ}$ to the semigroup $\struct {T, *}$.

Also see

 * Ordered Structure Monomorphism