A modular lattice is a lattice L = (L,∨,∧) that satisfies the modular identity: (( x∧z) ∨y) ∧z = ( x∧z) ∨( y∧z) .
A modular lattice is a lattice L = (L,∨,∧) that satisfies the modular law: x ≤ z ⇒ ( x∨y) ∧z ≤ x∨( y∧z) .
A modular lattice is a lattice L = (L,∨,∧) such that L has no sublattice isomorphic to the pentagon N5 =
Let L and M be modular lattices. A morphism from L to M is a function h : L→M that is a homomorphism: h(x∨y) = h(x)∨h(y) and h(x∧y) = h(x)∧h(y).
M3 = is the smallest nondistributive modular lattice. By a result of Dedekind  this lattice occurs as a sublattice of every nondistributive modular lattice.
|Congruence extension property||No|
|Definable principal congruences||No|
|Equationally definable principal congruences||No|
|Strong amalgamation property||No|
|Epimorphisms are surjective||No|