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In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa.

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rdf:type
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  • Semirretículo (es)
  • Semikekisi (in)
  • Semireticolo (it)
  • Semilattice (en)
  • Полурешётка (ru)
  • 半格 (zh)
rdfs:comment
  • In matematica un semireticolo è una struttura algebrica definibile come semigruppo commutativo idempotente. Una tale struttura si trova essere isomorfa ad un cosiddetto , insieme parzialmente ordinato nel quale ogni insieme di due elementi possiede massimo minorante (equivalentemente si potrebbe richiedere l'esistenza del minimo maggiorante). In effetti si può considerare la specie dei semireticoli come un della più nota e importante specie dei reticoli e ciascuna di queste strutture algebriche risulta criptomorfa ad una struttura relazionale, precisamente a un che ha come impoverimento un insieme semireticolato. (it)
  • Полурешётка (англ. semilattice, до 1960-х годов также использовался термин полуструктура) в общей алгебре — полугруппа, бинарная операция в которой коммутативна и идемпотентна. В терминах теории порядков полурёшетка может быть определена как частично упорядоченное множество, для каждой пары элементов которого определена точная верхняя грань (верхняя полурешётка) или точная нижняя грань (нижняя полурешётка). Множество, являющееся одновременно верхней и нижней полурешёткой, является решёткой. (ru)
  • 设是一个偏序集,若对于任意的,都有最小上界(并),或者对于任意的,都有最大下界(交),则称构成一个半格。 也可以将半格定义为一个代数结构。一个半格是一个代数结构或,其中和如同在格的定义中所述。 * 是满足运算是幂等的和交换的半群。 (zh)
  • En matemática, un semirretículo superior es un conjunto parcialmente ordenado en el que existe un supremo para todo subconjunto no vacío finito. Dualmente, un semirretículo inferior es un conjunto parcialmente ordenado en el que existe un ínfimo para todo subconjunto no vacío finito. Todo semirretículo superior es un semirretículo inferior en el orden inverso y vice versa. (es)
  • In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa. (en)
  • Dalam matematika, sambungan-semikekisi (atau semikekisi atas) adalah himpunan terurut parsial yang memiliki (batas atas terkecil) untuk himpunan bagian tidak kosong. , pertemuan-semikekisi (atau semikekisi bawah) adalah himpunan terurut parsial yang memiliki pertemuan (atau batas bawah terbesar) untuk himpunan bagian hingga yang tidak kosong. Setiap sambungan-semikekisi adalah pertemuan-semikekisi dalam dan sebaliknya. (in)
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