[Preprint] The plus construction with respect to subrings of the rationals.

IWe construct explicit models of universal Hℤ[J−1]-acyclic spaces , for any subset J of the prime numbers. The corresponding nullification functors provide thus plus construction functors for ordinary homology with ℤ[J−1] coefficients. Motivated by classical results about Quillen’s plus construction for integral homology, we prove that the Hℤ[J−1]-acyclization functor and the -cellularization functor coincide. We show that the acyclization-plus construction fiber sequence is always a cofiber sequence for simply connected spaces, but almost never so when the plus construction is not simply connected, unlike in the classical case.