\begin{definition}[Definition:Ordered Set of Subalgebras]
Let $L$ be an ordered set.
The '''ordered set of subalgebras''' of $L$ is ordered subset of $\operatorname{ClSystems}\left({L}\right)$ and is defined by
:$\operatorname{Subalgeras}\left({L}\right) := \left({X, \precsim}\right)$
where
:$X$ is the set of all directed suprema inheriting closure systems on $L$,
:$\operatorname{ClSystems}\left({L}\right)$ denotes the ordered set of closure systems on $L$.
\end{definition}