We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results, as well as a complete characterisation of structurally complete varieties of p-algebras.
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Kowalski et al. (2024) studied this question.
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