Definition:Pseudoprime (Order Theory)

Definition

Let $L = \struct {S, \vee, \wedge, \preceq}$ be an up-complete lattice.

Let $p \in S$.

Then $p$ is pseudoprime if and only if

there exists a prime ideal $P$ in $L$: $p = \sup P$

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article WAYBEL_7:def 6