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Semimodular lattice

In the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition: Semimodular lawa ∧ b <: a implies b <: a ∨ b.The notation a <: b means that bcoversa, i.e. a < b and there is no element c such that a < c < b. An atomistic semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids.

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