  Skew Boolean algebras (skew BA) and Boolean-like algebras (nBA) are
one-pointed and n-pointed noncommutative generalisation of Boolean algebras,
respectively. We show that any nBA is a cluster of n isomorphic right-handed
skew BAs, axiomatised here as the variety of skew star algebras. The variety of
skew star algebras is shown to be term equivalent to the variety of nBAs. We
use skew BAs in order to develop a general theory of multideals for nBAs. We
also provide a representation theorem for right-handed skew BAs in terms of
nBAs of n-partitions.
