Title: Inhabitants of interesting subsets of the Bousfield lattice,
Abstract: The set of Bousfield classes has some important subsets such as the
distributive lattice $\mathbf{DL}$ of all classes $\langle E\rangle$ which are
smash idempotent and the complete Boolean algebra $\mathbf{cBA}$ of closed
classes. We provide examples of spectra that are in $\mathbf{DL}$, but not in
$\mathbf{cBA}$; in particular, for every prime $p$, the Bousfield class of the
Eilenberg-MacLane spectrum $\langle
H\mathbb{F}_p\rangle\in\mathbf{DL}{\setminus}\mathbf{cBA}$.