Differences
This shows you the differences between two versions of the page.
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partially_ordered_groups [2010/07/29 15:46] 127.0.0.1 external edit |
partially_ordered_groups [2012/06/15 23:07] (current) jipsen |
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| Line 21: | Line 21: | ||
| $h(x \cdot y)=h(x) \cdot h(y)$, | $h(x \cdot y)=h(x) \cdot h(y)$, | ||
| $x\le y\Longrightarrow h(x)\le h(y)$ | $x\le y\Longrightarrow h(x)\le h(y)$ | ||
| - | |||
| - | ====Definition==== | ||
| - | A \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle | ||
| - | ...\rangle$ such that | ||
| - | |||
| - | $...$ is ...: $axiom$ | ||
| - | |||
| - | $...$ is ...: $axiom$ | ||
| ====Examples==== | ====Examples==== | ||
| - | Example 1: | + | Example 1: Any [[groups|group]] is a partially ordered group with equality as partial order. |
| ====Basic results==== | ====Basic results==== | ||
| Line 76: | Line 68: | ||
| ====Subclasses==== | ====Subclasses==== | ||
| - | [[Abelian partially ordered groups]] | + | [[Abelian partially ordered groups]] |
| - | [[Lattice-ordered groups]] expanded type | + | [[Lattice-ordered groups]] expanded type |
| ====Superclasses==== | ====Superclasses==== | ||
| - | [[Partially ordered monoids]] reduced type | + | [[Partially ordered monoids]] reduced type |
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