Order, lattices, ordered algebraic structures Distributive lattices Concept
Distributive lattice
Summary
A distributive lattice is a lattice in which meet and join distribute over each other. Lattices of sets and Boolean algebras are the main examples. The node distributive lattice gives the precise definition.
Where this leads
23 pages build on this one.
- Median algebra
- Ahlswede–Daykin inequality
- XYZ inequality
- Frame
- Birkhoff's representation theorem
- Prime ideal of a lattice
- Lattice of partitions
- Heyting algebra
- M3–N5 characterization of distributivity
- Esakia duality
- De Morgan algebra
- FKG inequality
- Stone algebra
- Congruence-distributive variety
- Diamond lattice M3
- Free distributive lattice
- Prime ideal theorem for distributive lattices
- Median algebra as a ternary algebra
- Residuated lattice
- Priestley duality
- Join-prime element
- Completely distributive lattice
- Congruence lattice problem
Further reading
About this page
| Tag | 0HM0HQCK6N |
|---|---|
| URI | m2://0HM0HQCK6N |
| Kind | concept |
| Writing | W2 usable |
| MSC | 06D05 |
| Same as |
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What this page needs for W3
- section Motivation: the question that the notion answers (0 of 1)
- section History: who introduced the notion and when (0 of 1)
- explanations for the audience (0 of 3)
- a person confirmed each agent-written section: rule P04 (0 of 1)
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What links here
Definitions
Used by
- Median algebra
- Ahlswede–Daykin inequality
- Frame
- Birkhoff's representation theorem
- Prime ideal of a lattice
- Heyting algebra
- M3–N5 characterization of distributivity
- De Morgan algebra
- FKG inequality
- Stone algebra
- Congruence-distributive variety
- Diamond lattice M3
- Free distributive lattice
- Prime ideal theorem for distributive lattices
- Median algebra as a ternary algebra
- Priestley duality
- Join-prime element
- Completely distributive lattice
- Congruence lattice problem
Results about this
- Ahlswede–Daykin inequality
- Birkhoff's representation theorem
- M3–N5 characterization of distributivity
- FKG inequality
- Prime ideal theorem for distributive lattices
- Priestley duality
Special cases
- De Morgan algebra
- Co-Heyting algebra
- Stone algebra
- Heyting algebra
- Free distributive lattice
- Generalized Boolean algebra