  The quotient class of a non-archimedean field is the set of cosets with
respect to all of its additive convex subgroups. The algebraic operations on
the quotient class are the Minkowski sum and product. We study the algebraic
laws of these operations. Addition and multiplication have a common structure
in terms of regular ordered semigroups. The two algebraic operations are
related by an adapted distributivity law.
