Prime filter of a distributive lattice

A prime filter is a proper lattice filter

P

such that

a \lor b \in P

implies

a \in P

or

b \in P

.

Table of contents
- Stone prime filter theorem Prime filter of a distributive lattice

Stone prime filter theorem

If a lattice filter

F

and lattice ideal

I

in a distributive lattice are disjoint, there is a prime filter of a distributive lattice containing

F

and disjoint from

I

.

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