  The mod-2 arithmetic Milnor invariants, introduced by Morishita, provide a
decomposition law for primes in canonical Galois extensions of $\mathbb{Q}$
with unitriangular Galois groups, and contain the Legendre and Redei symbols as
special cases. Morishita further proposed a notion of mod-q arithmetic Milnor
invariants, where q is a prime power, for number fields containing the q-th
roots of unity and satisfying certain class field theory assumptions. We extend
this theory from the number field context to general fields, by introducing a
notion of a linking invariant for discrete valuations and orderings. We further
express it as a Magnus homomorphism coefficient, and relate it to Massey
product elements in Galois cohomology.
