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\documentclass[12pt]{amsart}
\usepackage[pdfpagemode=Fullscreen,pdfstartview=FitBH]{hyperref}
\parindent=0pt
\parskip=5pt
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\addtolength{\textwidth}{1in}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem*{morphisms}{Morphisms}
\newtheorem*{basic_results}{Basic Results}
\newtheorem*{examples}{Examples}
\newtheorem{example}{}
\newtheorem*{properties}{Properties}
\newtheorem*{finite_members}{Finite Members}
\newtheorem*{subclasses}{Subclasses}
\newtheorem*{superclasses}{Superclasses}
\newcommand{\abbreviation}[1]{\textbf{Abbreviation: #1}}
\pagestyle{myheadings}\thispagestyle{myheadings}
\markboth{\today}{math.chapman.edu/structures}
\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}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\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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