Abstract
We mimick the construction of guard algebras and show how to extract a Church algebra out of the binary functions on an arbitrary algebra, containing a Church subalgebra of binary polynomial operations. We put to good use the weak Boolean product representations of these Church algebras 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 sufficient conditions for the stalks to be directly indecomposable. As an application, we prove that every skew Boolean algebra is a weak Boolean product of directly indecomposable skew Boolean algebras.
Dedicated to Don Pigozzi
on the occasion of his eightieth birthday
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Salibra, A., Ledda, A., Paoli, F. (2018). Boolean product representations of algebras via binary polynomials. In: Czelakowski, J. (eds) Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. Outstanding Contributions to Logic, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-74772-9_12
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