Complemented modular lattices

HomePage | RecentChanges | Preferences

Definition

A complemented modular lattice is a complemented lattice L = (L,∨,0,∧,1) that is modular:   (( xz) ∨y) ∧z = ( xz) ∨( yz) .

Morphisms

Let L and M be complemented modular lattices. A morphism from L to M is a function h : LM that is a bounded lattice homomorphism: h(xy) = h(x)∨h(y)  and  h(xy) = h(x)∧h(y)  and  h(0) = 0  and  h(1) = 1.

Some results

This class generates the same variety as the class of its finite members plus the non-desargean planes.

Properties

 Classtype first-order Equational theory decidable Quasiequational theory undecidable First-order theory undecidable Locally finite no Residual size unbounded Congruence distributive yes Congruence modular yes Congruence n-permutable yes Congruence regular no Congruence uniform no Congruence extension property Definable principal congruences Equationally definable principal congruences Amalgamation property Strong amalgamation property Epimorphisms are surjective

[Size 1]?:  1
[Size 2]?:  1
[Size 3]?:  0
[Size 4]?:  1
[Size 5]?:  1
[Size 6]?:
[Size 7]?:
[Size 8]?:

Boolean lattices

Superclasses

Bounded lattices
Modular lattices

HomePage | RecentChanges | Preferences