  Point sets of number-theoretic origin, such as the visible lattice points or
the $k$-th power free integers, have interesting geometric and spectral
properties and give rise to topological dynamical systems that belong to a
large class of subshifts with positive topological entropy. Among them are
$\cB$-free systems in one dimension and their higher-dimensional
generalisations, most prominently the $k$-free integers in algebraic number
fields. Here, we extend previous work on quadratic fields to the class of
cyclotomic fields. In particular, we discuss their entropy and extended
symmetries, with special focus on the interplay between dynamical and
number-theoretic notions.
