|
\Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} |
|
\Large Commutative lattice-ordered monoids \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Commutative_lattice-ordered_monoids}{edit} |
|
\abbreviation{Abbr} |
|
\abbreviation{CLMon} |
|
A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} |
|
A commutative lattice-ordered monoid is a \href{Lattice-ordered_monoids.pdf}{lattice-ordered monoid} $\mathbf{A}=\langle A, \vee, \wedge, \cdot, 1\rangle$ such that |
|
$op_1$ is (name of property): $axiom_1$ $op_2$ is ...: $...$ |
|
$\cdot$ is commutative: $xy=yx$ |
|
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 commutative lattice-ordered monoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(x \wedge y)=h(x) \wedge h(y)$, $h(x \cdot y)=h(x) \cdot h(y)$, $h(1)=1$. |
|
Classtype & (value, see description) \cite{Ln19xx} \\\hline |
|
Classtype & variety \\\hline |
|
Congruence distributive & \\\hline Congruence modular & \\\hline |
|
Congruence distributive & yes \\\hline Congruence modular & yes \\\hline |
|
\href{....pdf}{...} subvariety \href{....pdf}{...} expansion |
|
\href{Commutative_residuated_lattices.pdf}{Commutative residuated lattices} expansion |
|
\href{....pdf}{...} supervariety |
|
\href{Lattice-ordered_monoids.pdf}{Lattice-ordered monoids} supervariety |
|
\href{....pdf}{...} subreduct |
|
\href{Commutative_monoids.pdf}{Commutative monoids} subreduct |
|
\href{Commutative_lattice-ordered_semigroups.pdf}{Commutative lattice-ordered semigroups} subreduct |
![[Home]](/structures.gif)