An algebraic model for commutative Hℤ–algebras

We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of an arbitrary commutative ring R is equivalent to the homotopy category of E _∞-monoids in unbounded chain complexes over R. 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.