  We construct a four-term exact sequence which provides information on the
kernel and cokernel of the multiplication by a pure symbol in Milnor's K-theory
mod 2 of fields of characteristic zero. As an application we establish, for
fields of characteristics zero, the validity of three conjectures in the theory
of quadratic forms - the Milnor conjecture on the structure of the Witt ring,
the Khan-Rost-Sujatha conjecture and the J-filtration conjecture.
  The first version of this paper was written in the spring of 1996.
