A lattice is prime algebraic if every one if its elements is the limit of elements that are both coprime and compact.
Let be a complete lattice. Write for its set of compact and coprime elements.
Then is prime algebraic just if
Winskel, Glynn. 2009. ‘Prime Algebraicity’. Theoretical Computer Science 410 (41): 4160–68. https://doi.org/10.1016/j.tcs.2009.06.015.
@article{winskel_2009,
title = {Prime algebraicity},
volume = {410},
doi = {10.1016/j.tcs.2009.06.015},
number = {41},
journal = {Theoretical Computer Science},
author = {Winskel, Glynn},
year = {2009},
pages = {4160--4168},
}