meet-distributive lattice
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Distributive lattice — In mathematics, distributive lattices are lattices for which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set… … Wikipedia
Distributive lattice/Proofs — Lemma 1Every totally ordered set is a distributive lattice with max as join and min as meet.ProofWe will show: : x vee (y wedge z) = (x vee y)wedge(x vee z)We may suppose yle z (If not, zle y and we may switch y and z.) Recall that yle z is… … Wikipedia
distributive lattice — noun A lattice in which the meet and the join operations are distributive with respect to each other … Wiktionary
Lattice (order) — See also: Lattice (group) The name lattice is suggested by the form of the Hasse diagram depicting it. Shown here is the lattice of partitions of a four element set {1,2,3,4}, ordered by the relation is a refinement of . In mathematics, a… … Wikipedia
Lattice of subgroups — In mathematics, the lattice of subgroups of a group G is the lattice whose elements are the subgroups of G, with the partial order relation being set inclusion.In this lattice, the join of two subgroups is the subgroup generated by their union,… … Wikipedia
Residuated lattice — In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x le; y and a monoid x • y which admits operations x z and z / y loosely analogous to division or implication when x • y is viewed as… … Wikipedia
Modular lattice — Hasse diagram of N5, the smallest non modular lattice. In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self dual condition: Modular law x ≤ b implies… … Wikipedia
Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
Distributivity (order theory) — In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima. Most of these apply to partially ordered sets that are at least lattices, but the concept … Wikipedia
List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
Glossary of order theory — This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be … Wikipedia
