Mathematical Structures: History of Commutative residuated lattices

# History of Commutative residuated lattices

 Revision 5 . . July 8, 2004 2:04 pm by Jipsen Revision 4 . . July 8, 2004 2:02 pm by Jipsen Revision 3 . . April 6, 2003 1:52 pm by Peter Jipsen

Difference (from prior major revision) (author diff)

Changed: 32c32
 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
 A commutative residuated lattice is a \href{Residuated_lattices.pdf}{residuated lattice} $\mathbf{L}=\langle L, \vee, \wedge, \cdot, e, \backslash, /\rangle$ such that

Changed: 35c35
 $\cdot$ is commutative: $xy=yx$
 $\cdot$ is commutative: $xy=yx$

Changed: 46,49c46,47
 $h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)\ \mbox{and} h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)\$, $h(e)=e$
 $h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$, and $h(e)=e$