Category:Lattice theory
English: In mathematics, a lattice is a partially ordered set (also called a poset) in which any two elements have a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet). Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These "lattice-like" structures all admit order-theoretic as well as algebraic descriptions.
Category:Uses of Wikidata InfoboxCategory:Uses of Wikidata Infobox with no imagebranch of mathematics that studies order-theoretic lattices | |||||
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Pages in category "Category:Lattice theory"
- Lattice (order)
- Category:Boolean algebra
- Category:Divisibility lattice Hasse diagrams
- Category:Formal concept analysis
- Category:Heyting Algebra
- Category:Hypercube Hasse diagrams
- Category:Join and meet
- Category:Lattice of partitions of an order 4 set
- Category:Lattice of subgroups
- File:2d modular lattice.svg
- File:A De Morgan algebra.png
- File:Abstract interpretation of integers by signs svg.svg
- File:Abstract interpretation of integers by signs.pdf
- File:Antimatroid.svg
- File:Bands.svg
- File:Birkhoff representation theorem.gif
- File:Centred hexagon lattice D2.svg
- File:Diamond lattice.svg
- File:Diamond-by DrAK.svg
- File:Distributive lattice example.svg
- File:DistrSemilattice.svg
- File:DL Duality.png
- File:Dominance order partitions of 6.png
- File:Duale Verbaende.svg
- File:Dyck lattice D4.svg
- File:ExampleLattice.png
- File:Free distributive lattice with 3 generators (x,y,z).gif
- File:Free modular lattice with 3 generators (x,y,z).gif
- File:GaloisEmbeddings Complete Lattices.pdf
- File:Generalizations of abc.gif
- File:Hasse Diagram of Subgroup Lattice of D4.png
- File:Hexagon lattice.svg
- File:KeinVerband.svg
- File:Lattice 2.jpg
- File:Lattice M4.svg
- File:Lexicographic order on pairs of natural numbers.svg
- File:M 3 mit Beschriftung.svg
- File:M3 1xyz0.svg
- File:M3 abcde.svg
- File:M3 Lattice.png
- File:M3 linear terms.svg
- File:Metric lattice cube135.svg
- File:Monotonic but nonhomomorphic map between lattices.gif
- File:N 5 mit Beschriftung.svg
- File:N-Quadrat, gedreht.svg
- File:N5 1bax0.svg
- File:N5 1xyz0.svg
- File:N5 abcde.svg
- File:N5 Lattice.png
- File:N5 linear terms.svg
- File:N5 terms.svg
- File:Nat num x 2+.svg
- File:Nat num.svg
- File:NoLatticeDiagram.svg
- File:Non-dstrbtive lattices-warning.png
- File:Non-dstrbtive lattices-warning.svg
- File:Non-dstrbtive lattices.png
- File:Non-dstrbtive lattices.svg
- File:PairsOfSquaresLattice.gif
- File:Pairwise unifiable terms.gif
- File:Post lattice with constants.svg
- File:Post-lattice-constants.svg
- File:Post-lattice.png
- File:Post-lattice.svg
- File:Pow3nonlattice.svg
- File:Rehasse.png
- File:Ret1.png
- File:Ret2.png
- File:RetL.png
- File:RetL1.png
- File:RetM.png
- File:RetN5.png
- File:Retndistr.png
- File:Smallest nonmodular lattice 1.svg
- File:Smallest nonmodular lattice 2.svg
- File:Strict product order on pairs of natural numbers.svg
- File:Tevetlattice.jpg
- File:TwRepr-1.svg
- File:TwRepr-2.svg
- File:Verband monotonesBild.png
- File:Young5.svg