Bands

http://math.chapman.edu/structuresold/files/Bands.pdf

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Output written on Bands.pdf (2 pages, 57917 bytes).
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\begin{document}
\textbf{\Large Bands}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Bands}{edit}

\begin{definition}
A \emph{band} is a \href{Semigroups.pdf}{semigroup} $\mathbf{B}=\left\langle B,\cdot
\right\rangle $ such that

$\cdot $ is idempotent:  $x\cdot x=x$.
\end{definition}

\begin{morphisms}
Let $\mathbf{B}$ and $\mathbf{C}$ be 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 & no\\\hline
Congruence modular & no\\\hline
Congruence n-permutable & no\\\hline
Congruence regular & no\\\hline
Congruence uniform & no\\\hline
Congruence extension property & no\\\hline
Definable principal congruences & \\\hline
Equationally def. pr. cong. & \\\hline
Amalgamation property & no\\\hline
Strong amalgamation property & no\\\hline
Epimorphisms are surjective & \\\hline
\end{tabular}
\end{properties}
\end{table}
\begin{finite_members} $f(n)=$ number of members of size $n$.

$\begin{array}{lr}
f(1)= &1\\
f(2)= &3\\
f(3)= &10\\
f(4)= &46\\
f(5)= &251\\
f(6)= &1682\\
f(7)= &13213\\
\end{array}$
\end{finite_members}
\url{http://www.research.att.com/projects/OEIS?Anum=A058112}

\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\begin{subclasses}\ 

\href{Rectangular_bands.pdf}{Rectangular bands} 

\href{Semilattices.pdf}{Semilattices} 

\end{subclasses}
\begin{superclasses}\ 

\href{Semigroups.pdf}{Semigroups} 

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
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