  We show that the homotopy category of commutative algebra spectra over the
Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy
category of E-infinity-monoids in unbounded chain complexes. We do this by
establishing a chain of Quillen equivalences between the corresponding model
categories. We also provide a Quillen equivalence to commutative monoids in the
category of functors from the category of finite sets and injections to
unbounded chain complexes.
