Mathematical Structures: Complemented modular lattices

# Complemented modular lattices

http://mathcs.chapman.edu/structuresold/files/Complemented_modular_lattices.pdf
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\begin{document}
\textbf{\Large Complemented modular lattices}

\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}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
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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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