History of Complemented modular lattices

 
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 \begin{document}
 \textbf{\Large Complemented modular lattices}
 \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Complemented_modular_lattices}{edit}
 
 \abbreviation{CdMLat}
 \begin{definition}
 A \emph{complemented modular lattice} is a \href{Complemented_lattices.pdf}{complemented lattices} 
 $\mathbf{L}=\left\langle L,\vee ,0,\wedge ,1\right\rangle $ that is
 
 \href{Modular_lattices.pdf}{modular lattices}:  $(( x\wedge z) \vee y) \wedge z=( x\wedge z) \vee ( y\wedge z) $
 \end{definition}
 \begin{morphisms}
 Let $\mathbf{L}$ and $\mathbf{M}$ be complemented modular lattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ 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 $, $h(1)=1$
 \end{morphisms}
 \begin{basic_results}
 This class generates the same variety as the class of its finite
 members plus the non-desargean planes.
 \end{basic_results}
 \begin{examples}
 \begin{example}
 \end{example}
 \end{examples}
 \begin{table}[h]
 \begin{properties} (\href{http://math.chapman.edu/cgi-bin/structures?Properties}{description})
 
 \begin{tabular}{|ll|}\hline
 Classtype & first-order\\\hline
 Equational theory & decidable\\\hline
 Quasiequational theory & undecidable\\\hline
 First-order theory & undecidable\\\hline
 Locally finite & no\\\hline
 Residual size & unbounded\\\hline
 Congruence distributive & yes\\\hline
 Congruence modular & yes\\\hline
 Congruence n-permutable & yes\\\hline
 Congruence regular & no\\\hline
 Congruence uniform & no\\\hline
 Congruence extension property & \\\hline
 Definable principal congruences & \\\hline
 Equationally def. pr. cong. & \\\hline
 Amalgamation property & \\\hline
 Strong amalgamation property & \\\hline
 Epimorphisms are surjective & \\\hline
 \end{tabular}
 \end{properties}
 \end{table}
 \begin{finite_members} $f(n)=$ number of members of size $n$.
 
 $\begin{array}{lr}
 f(1)= &1\\
 f(2)= &1\\
 f(3)= &0\\
 f(4)= &1\\
 f(5)= &1\\
 f(6)= &\\
 f(7)= &\\
 f(8)= &\\
 \end{array}$
 \end{finite_members}
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 \begin{subclasses}\ 
 
 \href{Boolean_lattices.pdf}{Boolean lattices} 
 
 \end{subclasses}
 \begin{superclasses}\ 
 
 \href{Bounded_lattices.pdf}{Bounded lattices} 
 
 \href{Modular_lattices.pdf}{Modular lattices} 
 
 \end{superclasses}
 
 \begin{thebibliography}{10}
 
 \bibitem{Ln19xx}
 
 \end{thebibliography}
 
 \end{document}
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