I have been looking around for examples of $R$-bad spaced in the sense of Bousfield and Kan. In their book "Homotopy limits, completions and localizations] they give several examples of such spaces for $R = \mathbb{Z}/p$ (where $p$ is a prime) and also for $R = \mathbb{Z}$. But I my search for examples where $R$ is a subring of the rationals $\mathbb{Q}$ has been unfruitful so far. Does anybody know of such examples? Thanks!
