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A commutative residuated lattice is a \href{Residuated_lattices.pdf}{Residuated lattices} $\mathbf{L}=\left\langle L,\vee ,\wedge ,\cdot ,e,\backslash ,/\right\rangle $ such that |
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A commutative residuated lattice is a \href{Residuated_lattices.pdf}{residuated lattice} $\mathbf{L}=\langle L, \vee, \wedge, \cdot, e, \backslash, /\rangle $ such that |
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$\cdot $ is commutative: $xy=yx$ |
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$\cdot$ is commutative: $xy=yx$ |
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$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)\ \mbox{and} h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)\$, $ h(e)=e$ |
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$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$, and $h(e)=e$ |
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