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\Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} |
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\Large Lattice-ordered semigroups \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Lattice-ordered_semigroups}{edit} |
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\abbreviation{Abbr} |
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\abbreviation{LSgrp} |
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A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that |
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A lattice-ordered semigroup (or $\ell$-semigroup) is a structure $\mathbf{A}=\langle A\vee,\wedge,\cdot\rangle$ of type $\langle 2,2,2\rangle$ such that |
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$\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} |
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$\langle A,\vee,\wedge\rangle$ is a \href{Lattices.pdf}{lattice} |
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$op_1$ is name of property: $axiom_1$ |
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$\langle A,\cdot\rangle$ is a \href{Semigroups.pdf}{semigroups} |
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$op_2$ is ...: $...$ |
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$\cdot$ distributes over $\vee$: $x(y\vee z)=xy\vee xz$, $(x\vee y)z=xz\vee yz$ |
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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: $h(x ... y)=h(x) ... h(y)$ |
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Let $\mathbf{A}$ and $\mathbf{B}$ be lattice-ordered semigroups. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(x \wedge y)=h(x) \wedge h(y)$, $h(x \cdot y)=h(x) \cdot h(y)$, |
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Classtype & (value, see description) \cite{Lastname19xx} \\\hline |
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Classtype & variety \\\hline |
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Congruence distributive & \\\hline Congruence modular & \\\hline |
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Congruence distributive & yes\\\hline Congruence modular & yes\\\hline |
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\href{....pdf}{...} subvariety \href{....pdf}{...} expansion |
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\href{Lattice-ordered_monoids.pdf}{Lattice-ordered monoids} expanded type |
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\href{....pdf}{...} supervariety |
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\href{Semigroups.pdf}{Semigroups} reduced type |
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\href{....pdf}{...} subreduct |
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\href{Lattices.pdf}{Lattices} reduced type |
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