A complemented modular lattice is a complemented lattice L = (L,∨,0,∧,1) that is modular: (( x∧z) ∨y) ∧z = ( x∧z) ∨( y∧z) .
Let L and M be complemented modular lattices. A morphism from L to M is a function h : L→M that is a bounded lattice homomorphism: h(x∨y) = h(x)∨h(y) and h(x∧y) = h(x)∧h(y) and h(0) = 0 and h(1) = 1.
This class generates the same variety as the class of its finite members plus the non-desargean planes.
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences|
|Strong amalgamation property|
|Epimorphisms are surjective|