\begin{definition}[Definition:Pseudoprime (Order Theory)]
Let $L = \left({S, \vee, \wedge, \preceq}\right)$ be an up-complete lattice.
Let $p \in S$.
Then $p$ is '''pseudoprime''' {{iff}}
:there exists a prime ideal $P$ in $L$: $p = \sup P$
\end{definition}