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:

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

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 decidable undecidable undecidable no unbounded yes yes yes no no

Finite members

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