Boolean product representations of algebras via binary polynomials

We mimick the construction of guard algebras ([21], [2]) and show how to extract a Church algebra [13] out of the binary polynomials of an arbitrary algebra. We put to good use the weak Boolean product representations of these Church algebras of polynomials to obtain weak Boolean product representations of the original algebras. Although we cannot, in general, say much about the factors in these products, we identify a number of su¢cient conditions for the stalks to be directly indecomposable. As an application, we prove that every right-handed skew Boolean algebra is a weak Boolean product of directly indecomposable right-handed skew Boolean algebras.