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skew_lattices [2010/07/29 15:46]
127.0.0.1 external edit
skew_lattices [2012/06/23 19:21] (current)
jipsen
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A \emph{skew lattice}  is a structure $\mathbf{A}=\langle A,\vee,\wedge\rangle,$ of type $\langle 2,2\rangle$ such that A \emph{skew lattice}  is a structure $\mathbf{A}=\langle A,\vee,\wedge\rangle,$ of type $\langle 2,2\rangle$ such that
-$\langle A,\vee,\rangle$ is a [[band]],+$\langle A,\vee\rangle$ is a [[band]],
$\langle A,\wedge\rangle$ is a [[band]], $\langle A,\wedge\rangle$ is a [[band]],
and the following absorption laws hold:  $x\wedge (x\vee y)=x=x\vee (x\wedge y)$, $(x\vee y)\wedge y=y=(x\wedge y)\vee y$. and the following absorption laws hold:  $x\wedge (x\vee y)=x=x\vee (x\wedge y)$, $(x\vee y)\wedge y=y=(x\wedge y)\vee y$.
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-Remark: This is a template.
-If you know something about this class, click on the Edit text of this page'' link at the bottom and fill out this page.
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-It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.
==Morphisms== ==Morphisms==
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$h(x \vee y)=h(x) \vee h(y)$, $h(x \vee y)=h(x) \vee h(y)$,
$h(x \wedge y)=h(x) \wedge h(y)$, $h(x \wedge y)=h(x) \wedge h(y)$,
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-====Definition====
-A \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle -...\rangle$ such that
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-$...$ is ...:  $axiom$
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-$...$ is ...:  $axiom$
====Examples==== ====Examples====