“…For groups G and H, both G and H are always isomorphic to subgroups of G × H. As subgroups inherit all four of these properties, an easy extension of [10,Proposition 2.3], if G × H has one of these properties then so will both G and H. However, the situation for algebras in general, and for semigroups in particular, may not always be so straightforward. Indeed, in [13] de Witt was able to show that there exist monounary algebras A and B such that A is not residually finite but A × B is completely separable.…”