Mathematical Structures: Normal bands

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%%run pdflatex

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\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 Normal bands}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Normal_bands}{edit}

\abbreviation{NBand}
\begin{definition}
A \emph{normal band} is a \href{Bands.pdf}{bands} $\mathbf{B}=\langle B,\cdot
\rangle $ such that

$\cdot $ is normal: $x\cdot y\cdot z\cdot x=x\cdot z\cdot y\cdot x$.
\end{definition}
\begin{morphisms}
Let $\mathbf{B}$ and $\mathbf{C}$ be normal 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 $n$.

$\begin{array}{lr}
f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\
f(6)= &\\
f(7)= &\\
\end{array}$
\end{finite_members}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\begin{subclasses}\

\href{Rectangular_bands.pdf}{Rectangular bands}

\end{subclasses}
\begin{superclasses}\

\href{Bands.pdf}{Bands}

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
%

%%run pdflatex

%


\documentclass[12pt]{amsart}
\usepackage[pdfpagemode=Fullscreen,pdfstartview=FitBH]{hyperref}
\parindent=0pt
\parskip=5pt
\addtolength{\oddsidemargin}{-.5in}
\addtolength{\evensidemargin}{-.5in}
\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 Normal bands}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Normal_bands}{edit}

\abbreviation{NBand}
\begin{definition}
A \emph{normal band} is a \href{Bands.pdf}{bands} $\mathbf{B}=\langle B,\cdot
\rangle $ such that

$\cdot $ is normal: $x\cdot y\cdot z\cdot x=x\cdot z\cdot y\cdot x$.
\end{definition}
\begin{morphisms}
Let $\mathbf{B}$ and $\mathbf{C}$ be normal 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 $n$.

$\begin{array}{lr}
f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\
f(6)= &\\
f(7)= &\\
\end{array}$
\end{finite_members}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\begin{subclasses}\

\href{Rectangular_bands.pdf}{Rectangular bands}

\end{subclasses}
\begin{superclasses}\

\href{Bands.pdf}{Bands}

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
%


http://mathcs.chapman.edu/structuresold/files/Normal_bands.pdf
%%run pdflatex

%


\documentclass[12pt]{amsart}
\usepackage[pdfpagemode=Fullscreen,pdfstartview=FitBH]{hyperref}
\parindent=0pt
\parskip=5pt
\addtolength{\oddsidemargin}{-.5in}
\addtolength{\evensidemargin}{-.5in}
\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 Normal bands}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Normal_bands}{edit}

\abbreviation{NBand}
\begin{definition}
A \emph{normal band} is a \href{Bands.pdf}{bands} $\mathbf{B}=\langle B,\cdot
\rangle $ such that

$\cdot $ is normal:  $x\cdot y\cdot z\cdot x=x\cdot z\cdot y\cdot x$.
\end{definition}
\begin{morphisms}
Let $\mathbf{B}$ and $\mathbf{C}$ be normal 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 $n$.

$\begin{array}{lr}
f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\
f(6)= &\\
f(7)= &\\
\end{array}$
\end{finite_members}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\begin{subclasses}\ 

\href{Rectangular_bands.pdf}{Rectangular bands} 

\end{subclasses}
\begin{superclasses}\ 

\href{Bands.pdf}{Bands} 

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
%


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Last edited July 9, 2004 10:28 am by Jipsen (diff)
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