Multiplicative distance

In algebraic geometry, $$\mu$$ is said to be a multiplicative distance function over a field if it satisfies
 * $$\mu(AB)>1.\,$$
 * AB is congruent to A'B' iff $$\mu(AB)=\mu(A'B').\,$$
 * AB < A ' B '  iff $$\mu(AB)<\mu(A'B').\,$$
 * $$\mu(AB+CD)=\mu(AB)\mu(CD).\,$$