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- Modular_lattice 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. 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.".
- Modular_lattice thumbnail Smallest_nonmodular_lattice_1.svg?width=300.
- Modular_lattice wikiPageExternalLink 1206139232&page=record.
- Modular_lattice wikiPageExternalLink purl?GDZPPN002257947.
- Modular_lattice wikiPageExternalLink comm-rota.pdf.
- Modular_lattice wikiPageID "1089311".
- Modular_lattice wikiPageRevisionID "597842050".
- Modular_lattice first "L. A.".
- Modular_lattice first "T. S.".
- Modular_lattice hasPhotoCollection Modular_lattice.
- Modular_lattice id "2598".
- Modular_lattice id "m/m064460".
- Modular_lattice id "s/s084240".
- Modular_lattice last "Fofanova".
- Modular_lattice last "Skornyakov".
- Modular_lattice title "Modular lattice".
- Modular_lattice title "Semi-modular lattice".
- Modular_lattice subject Category:Lattice_theory.
- Modular_lattice 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. Modular lattices arise naturally in algebra and in many other areas of mathematics.".
- Modular_lattice label "Modular lattice".
- Modular_lattice label "Modularer Verband".
- Modular_lattice label "Retículo modular".
- Modular_lattice sameAs Modulární_svaz.
- Modular_lattice sameAs Modularer_Verband.
- Modular_lattice sameAs Retículo_modular.
- Modular_lattice sameAs m.03m3n00.
- Modular_lattice sameAs Q1538614.
- Modular_lattice sameAs Q1538614.
- Modular_lattice wasDerivedFrom Modular_lattice?oldid=597842050.
- Modular_lattice depiction Smallest_nonmodular_lattice_1.svg.
- Modular_lattice isPrimaryTopicOf Modular_lattice.