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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 Commutative residuated partially ordered semigroups \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Commutative_residuated_partially_ordered_semigroups}{edit} |
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\abbreviation{Abbr} |
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\abbreviation{CRPoSgrp} |
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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} |
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A commutative residuated partially ordered semigroup is a \href{Residuated_partially_ordered_semigroups.pdf}{residuated partially ordered semigroup} $\mathbf{A}=\langle A, \cdot, \to, \le\rangle$ such that |
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$op_1$ is (name of property): $axiom_1$ $op_2$ is ...: $...$ |
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$\cdot$ is commutative: $xy=yx$ |
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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 commutative residuated partially ordered monoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a orderpreserving homomorphism: $h(x \cdot y)=h(x) \cdot h(y)$, $h(x \to y)=h(x) \to h(y)$, and $x\le y\implies h(x)\le h(y)$. |
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Classtype & (value, see description) \cite{Ln19xx} \\\hline |
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Classtype & quasivariety \\\hline |
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\href{....pdf}{...} subvariety \href{....pdf}{...} expansion |
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\href{Commutative_residuated_lattice-ordered_semigroups.pdf}{Commutative residuated lattice-ordered semigroups} expanded type |
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\href{....pdf}{...} supervariety |
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\href{Residuated_partially_ordered_semigroups.pdf}{Residuated partially ordered semigroups} same type |
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\href{....pdf}{...} subreduct |
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\href{Commutative_partially_ordered_semigroups.pdf}{Commutative partially ordered semigroups} reduced type |
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