  Goodwillie's rational isomorphism between relative algebraic K-theory and
relative cyclic homology, together with the lambda decomposition of cyclic
homology, illustrates the close relationships among algebraic K-theory, cyclic
homology, and differential forms. In this paper, I prove a Goodwillie-type
theorem for relative Milnor $K$-theory, working over a very general class of
commutative rings, defined via the stability criterion of Van der Kallen. Early
results of Van der Kallen and Bloch are special cases. The result likely
generalizes in terms of de Rahm-Witt complexes, by weakening some invertibility
assumptions, but the class of rings considered is already more than
sufficiently general for the intended applications. The main motivation for
this paper arises from applications to the infinitesimal theory of Chow groups,
first pointed out by Bloch in the 1970's, and prominent in recent work of Green
and Griffiths. Related results and geometric applications are discussed in the
final section.
