as semimodular lattices.

A semimodular lattice is one kind of algebraic lattice.

Birkhoff's condition

A lattice is sometimes called weakly semimodular if it satisfies the following condition due to Garrett Birkhoff:;Birkhoff's condition: If a ? b <: a and a ? b <: b,
:then a <: a ? b and b <: a ? b.Every semimodular lattice is weakly semimodular. The converse is true for lattices of finite length, and more generally for upper continuous (meets distribute over joins of chains) relatively atomic lattices.

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