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- Q1538614 subject Q8480477.
- Q1538614 abstract "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 x ∨ (a ∧ b) = (x ∨ a) ∧ b,where ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. For an intuition behind the modularity condition see and below.Modular lattices arise naturally in algebra and in many other areas of mathematics. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice.Every distributive lattice is modular.In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary elements a and x (≤ b). Such an element is called a modular element. Even more generally, the modular law may hold for a fixed pair (a, b). Such a pair is called a modular pair, and there are various generalizations of modularity related to this notion and to semimodularity.".
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- Q1538614 wikiPageWikiLink Q8480477.
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- Q1538614 type Thing.
- Q1538614 comment "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 x ∨ (a ∧ b) = (x ∨ a) ∧ b,where ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. For an intuition behind the modularity condition see and below.Modular lattices arise naturally in algebra and in many other areas of mathematics.".
- Q1538614 label "Modular lattice".
- Q1538614 differentFrom Q2794475.
- Q1538614 depiction N5_1bax0.svg.