DBpedia – Linked Data Fragments

Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Modular_lattice> ?p ?o }

• 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. 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.".
• Modular_lattice thumbnail N5_1bax0.svg?width=300.
• Modular_lattice wikiPageExternalLink 1206139232&page=record.
• Modular_lattice wikiPageExternalLink comm-rota.pdf.
• Modular_lattice wikiPageID "1089311".
• Modular_lattice wikiPageLength "14335".
• Modular_lattice wikiPageOutDegree "36".
• Modular_lattice wikiPageRevisionID "681837333".
• Modular_lattice wikiPageWikiLink Abelian_group.
• Modular_lattice wikiPageWikiLink Algebra.
• Modular_lattice wikiPageWikiLink Ascending_chain_condition.
• Modular_lattice wikiPageWikiLink Associative_property.
• Modular_lattice wikiPageWikiLink Cambridge_University_Press.
• Modular_lattice wikiPageWikiLink Category:Lattice_theory.
• Modular_lattice wikiPageWikiLink Complemented_lattice.
• Modular_lattice wikiPageWikiLink Correspondence_theorem_(group_theory).
• Modular_lattice wikiPageWikiLink Distributive_lattice.
• Modular_lattice wikiPageWikiLink Duality_(order_theory).
• Modular_lattice wikiPageWikiLink Group_(mathematics).
• Modular_lattice wikiPageWikiLink Isomorphism_theorem.
• Modular_lattice wikiPageWikiLink Join_and_meet.
• Modular_lattice wikiPageWikiLink Lattice_(order).
• Modular_lattice wikiPageWikiLink Lattice_of_subgroups.
• Modular_lattice wikiPageWikiLink Maximal_element.
• Modular_lattice wikiPageWikiLink Module_(mathematics).
• Modular_lattice wikiPageWikiLink Normal_subgroup.
• Modular_lattice wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
• Modular_lattice wikiPageWikiLink Order_theory.
• Modular_lattice wikiPageWikiLink Partially_ordered_set.
• Modular_lattice wikiPageWikiLink Richard_Dedekind.
• Modular_lattice wikiPageWikiLink Semimodular_lattice.
• Modular_lattice wikiPageWikiLink Universal_algebra.
• Modular_lattice wikiPageWikiLink Variety_(universal_algebra).
• Modular_lattice wikiPageWikiLink Vector_space.
• Modular_lattice wikiPageWikiLink Young–Fibonacci_lattice.
• Modular_lattice wikiPageWikiLink File:Centred_hexagon_lattice_D2.svg.
• Modular_lattice wikiPageWikiLink File:Free_modular_lattice_with_3_generators_(x,y,z).gif.
• Modular_lattice wikiPageWikiLink File:N5_1bax0.svg.
• Modular_lattice wikiPageWikiLink File:Smallest_nonmodular_lattice_2.svg.
• Modular_lattice wikiPageWikiLinkText "M-symmetric".
• Modular_lattice wikiPageWikiLinkText "Modular lattice".
• Modular_lattice wikiPageWikiLinkText "Modular lattice#Diamond isomorphism theorem".
• Modular_lattice wikiPageWikiLinkText "Modular lattice#Modular pairs and related notions".
• Modular_lattice wikiPageWikiLinkText "modular element".
• Modular_lattice wikiPageWikiLinkText "modular lattice".
• Modular_lattice wikiPageWikiLinkText "modular law".
• Modular_lattice wikiPageWikiLinkText "modular".
• Modular_lattice first "L. A.".
• Modular_lattice first "T. S.".
• 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 wikiPageUsesTemplate Template:Citation.
• Modular_lattice wikiPageUsesTemplate Template:Cn.
• Modular_lattice wikiPageUsesTemplate Template:Distinguish.
• Modular_lattice wikiPageUsesTemplate Template:Lang-de.
• Modular_lattice wikiPageUsesTemplate Template:Planetmath_reference.
• Modular_lattice wikiPageUsesTemplate Template:Rp.
• Modular_lattice wikiPageUsesTemplate Template:Springer.
• Modular_lattice subject Category:Lattice_theory.
• Modular_lattice hypernym Lattice.
• Modular_lattice type ArchitecturalStructure.
• Modular_lattice type Thing.
• 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. For an intuition behind the modularity condition see and below.Modular lattices arise naturally in algebra and in many other areas of mathematics.".
• Modular_lattice label "Modular lattice".
• Modular_lattice differentFrom Unimodular_lattice.
• Modular_lattice sameAs Q1538614.
• Modular_lattice sameAs Modulární_svaz.
• Modular_lattice sameAs Modularer_Verband.
• Modular_lattice sameAs Retículo_modular.
• Modular_lattice sameAs 모듈러_격자.
• Modular_lattice sameAs m.03m3n00.
• Modular_lattice sameAs Модулярна_ґратка.
• Modular_lattice sameAs Q1538614.
• Modular_lattice wasDerivedFrom Modular_lattice?oldid=681837333.
• Modular_lattice depiction N5_1bax0.svg.
• Modular_lattice isPrimaryTopicOf Modular_lattice.