Modular lattice
In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular lawa ≤ b implies a ∨ (x ∧ b) = (a ∨ x) ∧ b where x, a, b are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice [a, b], a fact known as the diamond isomorphism theorem. An alternative but equivalent condition stated as an equation (see below) emphasizes that modular lattices form a variety in the sense of universal algebra.
Algebraic structureAssociated graded ringComplemented latticeCongruence lattice problemContinuous geometryCorrespondence theorem (group theory)Decomposition of a moduleDedekind latticeDedekind–MacNeille completionDiamond isomorphism theoremDiamond theoremDistributive latticeFree objectIdeal (ring theory)Introduction to Lattices and OrderIwasawa groupJohn_von_NeumannJordan operator algebraLattice of subgroupsLinear subspaceList of first-order theoriesList of order theory topicsM-symmetric latticeMap of latticesModular graphModular latticeModular lawModular pairModular subgroupModuleModule (mathematics)N5Normal subgroupProduct of group subsetsQuotient (universal algebra)Richard DedekindSemimodular latticeSubsumption latticeSupersolvable arrangementThomas H. Brylawski
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Modular lattice
In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular lawa ≤ b implies a ∨ (x ∧ b) = (a ∨ x) ∧ b where x, a, b are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice [a, b], a fact known as the diamond isomorphism theorem. An alternative but equivalent condition stated as an equation (see below) emphasizes that modular lattices form a variety in the sense of universal algebra.
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Ein modularer Verband im Sinne ...... e auf diesen Begriff aufbauen.
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In the branch of mathematics c ...... ered the modular identity in .
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Modulární svazy jsou typy svaz ...... ější podmínku tzv. modularity.
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Un retículo modular en el sent ...... ridad relacionadas con el de .
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Модулярна ґратка — ґратка, яка ...... називається модулярною парою.
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Модулярная решётка (дедекиндов ...... хардом Дедекиндом в 1894 году.
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순서론에서, 모듈러 격자(영어: modular lattice)는 일종의 약한 결합 법칙을 만족시키는 격자이다.
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L. A.
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T. S.
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Fofanova
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Skornyakov
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title
Modular lattice
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Semi-modular lattice
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Ein modularer Verband im Sinne ...... tributive Verband ist modular.
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In the branch of mathematics c ...... he sense of universal algebra.
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Modulární svazy jsou typy svaz ...... ější podmínku tzv. modularity.
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Un retículo modular en el sent ...... ículo distributivo es modular.
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Модулярна ґратка — ґратка, яка ...... рибутивна ґратка є модулярною.
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Модулярная решётка (дедекиндов ...... жит его в качестве подрешётки.
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순서론에서, 모듈러 격자(영어: modular lattice)는 일종의 약한 결합 법칙을 만족시키는 격자이다.
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Modular lattice
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Modularer Verband
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Modulární svaz
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Retículo modular
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Модулярна ґратка
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Модулярная решётка
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모듈러 격자
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