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ordered_monoids_with_zero [2010/07/29 15:46] external edit
ordered_monoids_with_zero [2016/11/26 17:01] (current)
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$0$ is a \emph{zero}:  $x\cdot 0 = 0$ and $0\cdot x = 0$ $0$ is a \emph{zero}:  $x\cdot 0 = 0$ and $0\cdot x = 0$
-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. 
-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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$h(0)=0$, $h(0)=0$,
$x\le y\Longrightarrow h(x)\le h(y)$. $x\le y\Longrightarrow h(x)\le h(y)$.
-A \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle 
-...\rangle$ such that 
-$...$ is ...:  $axiom$ 
-$...$ is ...:  $axiom$ 
====Examples==== ====Examples====
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====Subclasses==== ====Subclasses====
-  [[Commutative ordered monoids]]+[[Commutative ordered monoids]]
====Superclasses==== ====Superclasses====
-  [[Ordered monoids]] reduced type+[[Ordered monoids]] reduced type
-  [[Ordered semigroups with zero]] reduced type+[[Ordered semigroups with zero]] reduced type
-  [[Representable residuated lattices]]+[[Representable residuated lattices]]