  Hazewinkel proved the Ditters conjecture that the algebra of quasisymmetric
functions over the integers is free commutative by constructing a nice
polynomial basis. In this paper we prove a structure theorem for the algebra of
peak quasisymmetric functions (PQSym) over the integers. It provides a
polynomial basis of PQSym over the rational field, different from Hsiao's
basis, and implies the freeness of PQSym over its subring of symmetric
functions spanned by Schur's Q-functions.
