# Differences

This shows you the differences between two versions of the page.

ordered_monoids_with_zero [2010/07/29 15:46] 127.0.0.1 external edit |
ordered_monoids_with_zero [2016/11/26 17:01] (current) jipsen |
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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 $0\cdot x = 0$ | ||

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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. | ||

- | |||

- | 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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$h(0)=0$, | $h(0)=0$, | ||

$x\le y\Longrightarrow h(x)\le h(y)$. | $x\le y\Longrightarrow h(x)\le h(y)$. | ||

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- | ====Definition==== | ||

- | 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]] |

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