### Relative reciprocities on Dedekind domains and the K_2 of a field, by Frans Keune

The author's proof in 1974 of Matsumoto's presentation of the K_{2} of
a field was based on Bass' description of the SK_{1} of an ideal in a
Dedekind domain by relative reciprocities together with a reciprocity law for
the Milnor ring of a field. Here it is shown that with the use of general exact
sequences in algebraic K-theory this description of the SK_{1} of an
ideal in a Dedekind domain is easily derived. A proof of Matsumoto's theorem
that does not use the Milnor ring is given here as well.

Frans Keune <keune@math.ru.nl>