Homological localizations of Eilenberg-Mac Lane spectra

We discuss the Bousfield localization $L_{E}X$ for any spectrum $E$ and any $HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property of $HR$-modules, it is enough to study the localization of Eilenberg-Mac Lane spectra. Using general results about stable $f$-localizations, we give a method to compute the localization of an Eilenberg-Mac Lane spectrum $L_{E}HG$ for any spectrum $E$ and any abelian group $G$. We describe $L_{E}HG$ explicitly when $G$ is one of the following: finitely generated abelian groups, $p$-adic integers, Pr"ufer groups, and subrings of the rationals. The results depend basically on the $E$-acyclicity patterns of the spectrum $H\text{Q}$ and the spectrum $H\mathbb{Z}\mathrm{/}p$ for each prime $p$.