Definition 1. Let $G$ be a group and $\leq$ be an order. $G$ is ordered by $\leq$ if multiplication preserves the order, i.e. for all $a$, $b$, $x \in G$,
\[a \leq b \enspace\rimp\enspace ax \leq bx \,\land\, xa \leq xb.\]Pub Mar 20, 2026 Up Jun 11, 2026
Definition 1. Let $G$ be a group and $\leq$ be an order. $G$ is ordered by $\leq$ if multiplication preserves the order, i.e. for all $a$, $b$, $x \in G$,
\[a \leq b \enspace\rimp\enspace ax \leq bx \,\land\, xa \leq xb.\]