\begin{definition}[Definition:Ordered Structure]
An '''ordered structure''' $\struct {S, \circ, \preceq}$ is an algebraic system such that:
:$(1): \quad \struct {S, \circ}$ is an algebraic structure
:$(2): \quad \struct {S, \preceq}$ is an ordered set
:$(3): \quad \preceq$ is compatible with $\circ$.
There are various breeds of ordered structure the same way that there are for algebraic structures:
\end{definition}