History of Distributive p-algebras

 
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 \begin{document}
 \textbf{\Large Distributive p-algebras}
 \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Distributive_p-algebras}{edit}
 
 \abbreviation{DpAlg}
 \begin{definition}
 A \emph{distributive p-algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle $ such that
 
 
 $\langle L,\vee,0,\wedge,1\rangle $ is a \href{Bounded_distributive_lattices.pdf}{bounded distributive lattices}
 
 
 $x^*$ is the \emph{pseudo complement} of $x$:  $y\leq x^* \iff x\wedge y=0$
 
 \end{definition}
 \begin{morphisms}
 Let $\mathbf{L}$ and $\mathbf{M}$ be distributive p-algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a
 homomorphism: 
 
 $h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$, $h(x^*)=h(x)^*$
 
 \end{morphisms}
 \begin{basic_results}
 \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 & variety\\\hline
 Equational theory & decidable\\\hline
 Quasiequational theory & \\\hline
 First-order theory & \\\hline
 Congruence distributive & yes\\\hline
 Congruence modular & yes\\\hline
 Congruence n-permutable & \\\hline
 Congruence regular & \\\hline
 Congruence uniform & \\\hline
 Congruence extension property & \\\hline
 Definable principal congruences & \\\hline
 Equationally def. pr. cong. & \\\hline
 Amalgamation property & yes\\\hline
 Strong amalgamation property & \\\hline
 Epimorphisms are surjective & \\\hline
 Locally finite & \\\hline
 Residual size & \\\hline
 \end{tabular}
 \end{properties}
 \end{table}
 \begin{finite_members} $f(n)=$ number of members of size $n$.
 
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 \begin{subclasses}\ 
 
 \href{Distributive_double_p-algebras.pdf}{Distributive double p-algebras} 
 
 \end{subclasses}
 \begin{superclasses}\ 
 
 \href{Distributive_lattices.pdf}{Distributive lattices} 
 
 \end{superclasses}
 
 \begin{thebibliography}{10}
 
 \bibitem{Ln19xx}
 
 \end{thebibliography}
 
 \end{document}
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