Partially ordered group
GROUP WITH A COMPATIBLE PARTIAL ORDER
Lattice ordered group; Positive element (ordered group); Partially ordered monoid; Orderable group; Ordered group; Lattice-ordered group; Partially-ordered group; Integrally closed ordered group; Integrally closed partially ordered group; Integrally closed (partially ordered group); Positive cone of a partially ordered group
In abstract algebra, a partially ordered group is a group (G, +) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a + g ≤ b + g and g + a ≤ g + b.