=====Complemented modular lattices=====

Abbreviation: **CdMLat**
====Definition====
A \emph{complemented modular lattice} is a [[complemented lattices]] 
$\mathbf{L}=\langle L,\vee ,0,\wedge ,1\rangle $ that is

[[modular lattices]]:  $(( x\wedge z) \vee y) \wedge z=( x\wedge z) \vee ( y\wedge z) $
==Morphisms==
Let $\mathbf{L}$ and $\mathbf{M}$ be complemented modular lattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\to M$ that is a
bounded lattice homomorphism: 

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$
====Examples====
Example 1: 

====Basic 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 def. pr. cong.]]  | |
^[[Amalgamation property]]  | |
^[[Strong amalgamation property]]  | |
^[[Epimorphisms are surjective]]  | |
====Finite members====

$\begin{array}{lr}
f(1)= &1\\
f(2)= &1\\
f(3)= &0\\
f(4)= &1\\
f(5)= &1\\
f(6)= &\\
f(7)= &\\
f(8)= &\\
\end{array}$

====Subclasses====
[[Boolean lattices]] 

====Superclasses====
[[Bounded lattices]] 

[[Modular lattices]] 


====References====

[(Ln19xx>
)]