# Differences

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

partially_ordered_groups [2010/07/29 15:46]
127.0.0.1 external edit
partially_ordered_groups [2012/06/15 23:07] (current)
jipsen
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