Mathematical Structures: History of Monadic algebras

 Revision 2 . . July 29, 2004 12:50 am by Jipsen Revision 1 . . July 9, 2004 10:19 am by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,30c28,29
 \Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line

Changed: 32c31
 \abbreviation{Abbr}
 \abbreviation{MonA}

Changed: 35,36c34
 A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that
 A monadic algebra is a structure $\mathbf{A}=\langle A, \vee, 0, \wedge, 1, \neg, f\rangle$ of type $\langle 2, 0, 2, 0, 1, 1\rangle$ such that

Changed: 38c36
 $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class}
 $\langle A, \vee, 0, \wedge, 1, \neg\rangle$ is a \href{Boolean_algebras.pdf}{Boolean algebra}

Changed: 40c38
 $op_1$ is (name of property): $axiom_1$
 $f$ is a unary closure operator: $f(x\vee y)=f(x)\vee f(y)$, $f(0)=0$, $x\le f(x)=f(f(x))$

Changed: 42c40
 $op_2$ is ...: $...$
 $f$ is self conjugated: $f(x)\wedge y=0\iff x\wedge f(y)=0$

Changed: 51,52c49,52
 Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$
 Let $\mathbf{A}$ and $\mathbf{B}$ be monodic algebras. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(\neg x)=\neg h(x)$, $h(f(x))=f(h(x))$.

Changed: 78,79c78,79
 Classtype & (value, see description) \cite{Ln19xx} \\\hline Equational theory & \\\hline
 Classtype & variety \\\hline Equational theory & decidable\\\hline

Changed: 84,92c84,92
 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
 Congruence distributive & yes\\\hline Congruence modular & yes\\\hline Congruence $n$-permutable & yes, $n=2$\\\hline Congruence regular & yes\\\hline Congruence uniform & yes\\\hline Congruence extension property & yes\\\hline Definable principal congruences & yes\\\hline Equationally def. pr. cong. & yes\\\hline Amalgamation property & yes\\\hline

Changed: 103c103
 f(2)= &\\
 f(2)= &1\\

Changed: 128c128
 \href{....pdf}{...} supervariety
 \href{Boolean_algebras.pdf}{Boolean algebras} reduced type

Changed: 130c130
 \href{....pdf}{...} subreduct
 \href{Closure_algebras.pdf}{Closure algebras}

Changed: 136c136
 \bibitem{Ln19xx}
 \bibitem{Lastname19xx}