History of Rectangular bands

 
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 \begin{document}
 \textbf{\Large Rectangular bands}
 \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Rectangular_bands}{edit}
 
 \abbreviation{RBand}
 \begin{definition}
 A \emph{rectangular band} is a \href{Bands.pdf}{bands} $\mathbf{B}=\langle B,\cdot
 \rangle $ such that
 
 $\cdot $ is rectangular:  $x\cdot y\cdot x=x$.
 \end{definition}
 \begin{definition}
 A \emph{rectangular band} is a \href{Bands.pdf}{bands} $\mathbf{B}=\langle B,\cdot
 \rangle $ such that
 
 $x\cdot y\cdot z=x\cdot z$.
 \end{definition}
 \begin{morphisms}
 Let $\mathbf{B}$ and $\mathbf{C}$ be rectangular bands. A morphism from $\mathbf{B}$
 to $\mathbf{C}$ is a function $h:B\rightarrow C$ that is a homomorphism: 
 
 $h(xy)=h(x)h(y)$
 
 \end{morphisms}
 \begin{basic_results}
 \end{basic_results}
 \begin{examples}
 \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 in polynomial time\\\hline
 Quasiequational theory & \\\hline
 First-order theory & \\\hline
 Locally finite & yes\\\hline
 Residual size & \\\hline
 Congruence distributive & \\\hline
 Congruence modular & \\\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 & \\\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)= &\\
 f(3)= &\\
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 \end{finite_members}
 \hyperbaseurl{http://math.chapman.edu/structures/files/}
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 \begin{subclasses}\ 
 
 \href{Left-zero_semigroups.pdf}{Left-zero semigroups} 
 
 \href{Right-zero_semigroups.pdf}{Right-zero semigroups} 
 
 \end{subclasses}
 \begin{superclasses}\ 
 
 \href{Normal_bands.pdf}{Normal bands} 
 
 \end{superclasses}
 
 \begin{thebibliography}{10}
 
 \bibitem{Ln19xx}
 
 \end{thebibliography}
 
 \end{document}
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