The Stone representation
theory provides a canonical method whereby each Boolean algebra A can be
embedded isomorphically in a complete, atomistic Boolean algebra A∗. Jonsson and
Tarski have shown how each additive operation (of any number of places) on A can
be extended canonically to a completely additive operation on A∗, in such a way that
whenever an equation involving given additive operations holds identically in A, the
corresponding equation involving the canonical extensions of those operations
will hold identically in A∗. In this paper we present a generalization of this
result.
