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In mathematics, a distributive lattice is a lattice in 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 union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to isomorphism—given as such a lattice of sets.

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type
label
  • Distributive lattice
  • Distributiver Verband
  • Distributivní svaz
  • Retículo distributivo
  • Дистрибутивна ґратка
  • 分配格
  • 분배 격자
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  • En matemática, un retículo distributivo es un retículo en el cual las operaciones de unión (join) e intersección (meet) se distribuyen la una sobre la otra. El ejemplo típico de estas estructuras es una colección de conjuntos, donde los operadores quedan dados por la unión de conjuntos y la intersección de conjuntos. De hecho, dicho ejemplo describe el escenario por completo: todo retículo distributivo es isomorfo a un retículo de conjuntos.
  • 设是一个格，若对于任意的有 则称为分配格。 上述两个等式互为对偶式，根据格的对偶原理，在证明一个格是分配格时只需证明其中任意一个等式即可。 设是一个格，为分配格当且仅当对于任意的，若且，则。
  • 순서론에서 분배 격자(分配格子, 영어: distributive lattice)는 만남과 이음이 서로 분배 법칙을 따르는 격자이다. 모든 분배 격자는 항상 집합들의 포함 관계에 따른 격자로 나타낼 수 있다.
  • In mathematics, a distributive lattice is a lattice in 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 union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to isomorphism—given as such a lattice of sets.
  • Дистрибутивна ґратка — ґратка, в якій справедлива тотожність рівносильна тотожності та
  • Distributivní svaz je v matematice označení svazu, jehož dvě operace jsou vzájemně distributivní.
  • Ein distributiver Verband ist eine spezielle Struktur der Mathematik. Gegenüber allgemeinen Verbänden, in denen für die beiden (zweistelligen) Operationen und nur die Assoziativgesetze, die Kommutativgesetze und die Absorptionsgesetze gefordert werden, gelten in einem distributiven Verband noch zusätzlich Distributivgesetze für beide Richtungen.
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