Prime algebraic lattice

A lattice is prime algebraic if every one if its elements is the limit of elements that are both coprime and compact.

Definition

Let (L, \sqsubseteq) be a complete lattice. Write \mathsf{K}_{co}(L) for its set of compact and coprime elements.

Then L is prime algebraic just if

  d = \bigsqcup \{ c \in \mathsf{K}_{co}(L) \mid c \sqsubseteq d \}

See also

• Algebraic lattice

References

@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},
}