Partially ordered group
= Partially ordered group
{wiki}
= Ordered group
{synonym}
A <group> with a <partial order> preserved by multiplication on both sides: $a\le b$ implies $xay\le xby$ for all $x,y$. In additive notation this says $a\le b\Rightarrow x+a+y\le x+b+y$. Preserving only one side is a different orderability condition.