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- Semimodular_lattice abstract "In the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition:Semimodular law a ∧ b <: a implies b <: a ∨ b.The notation a <: b means that b covers a, i.e. a < b and there is no element c such that a < c < b.An atomistic (hence algebraic) semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids. An atomistic semimodular bounded lattice of finite length is called a geometric lattice and corresponds to a matroid of finite rank.Semimodular lattices are also known as upper semimodular lattices; the dual notion is that of a lower semimodular lattice. A finite lattice is modular if and only if it is both upper and lower semimodular.A finite lattice, or more generally a lattice satisfying the ascending chain condition or the descending chain condition, is semimodular if and only if it is M-symmetric. Some authors refer to M-symmetric lattices as semimodular lattices.".
- Semimodular_lattice thumbnail Centred_hexagon_lattice_D2.svg?width=300.
- Semimodular_lattice wikiPageID "13881586".
- Semimodular_lattice wikiPageRevisionID "545007267".
- Semimodular_lattice first "T. S.".
- Semimodular_lattice hasPhotoCollection Semimodular_lattice.
- Semimodular_lattice id "7286".
- Semimodular_lattice id "s/s084240".
- Semimodular_lattice last "Fofanova".
- Semimodular_lattice title "Semi-modular lattice".
- Semimodular_lattice title "Semimodular lattice".
- Semimodular_lattice subject Category:Lattice_theory.
- Semimodular_lattice comment "In the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition:Semimodular law a ∧ b <: a implies b <: a ∨ b.The notation a <: b means that b covers a, i.e. a < b and there is no element c such that a < c < b.An atomistic (hence algebraic) semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids.".
- Semimodular_lattice label "Semimodular lattice".
- Semimodular_lattice label "Semimodularer Verband".
- Semimodular_lattice sameAs Semimodularer_Verband.
- Semimodular_lattice sameAs m.043v05c.
- Semimodular_lattice sameAs Q1748671.
- Semimodular_lattice sameAs Q1748671.
- Semimodular_lattice wasDerivedFrom Semimodular_lattice?oldid=545007267.
- Semimodular_lattice depiction Centred_hexagon_lattice_D2.svg.
- Semimodular_lattice isPrimaryTopicOf Semimodular_lattice.