Let F be a skew field with a valuation (also called total) subring B, i.e. x in F\ B implies x-1
in B. Such rings are useful not only in the investigation and construction of division algebras (see for example ,,) but also in geometry ().
Associated with B is an invariant subring R of F and a value group G. We investigate the relationship between properties like the distributivity of R and properties like being lattice ordered of G.