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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 ordered semigroups \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Commutative_ordered_semigroups}{edit} |
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\abbreviation{Abbr} |
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\abbreviation{COSgrp} |
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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 ordered semigroups is an \href{Ordered_semigroups.pdf}{ordered semigroup} $\mathbf{A}=\langle A,\cdot,\le\rangle$ 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 ordered semigroups. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a orderpreserving homomorphism: $h(x \cdot y)=h(x) \cdot h(y)$ and $x\le y\implies h(x)\le h(y)$ |
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\href{....pdf}{...} subvariety \href{....pdf}{...} expansion |
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\href{Commutative_ordered_monoids.pdf}{Commutative ordered monoids} expansion |
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\href{....pdf}{...} supervariety |
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\href{Ordered_semigroups.pdf}{Ordered semigroups} supervariety |
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\href{....pdf}{...} subreduct |
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\href{Commutative_semigroups.pdf}{Commutative semigroups} subreduct |
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