Homotopical localizations of module spectra

We prove that stable f f -localizations (where f f is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg–Mac Lane spectrum H Z H{\mathbb {Z}} . As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations.