A note on subdirectly irreducible distributive double p-algebras
M. E. Adams, Tibor Katriňák · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1983
Abstract A regular double p-algebra L satisfying (i) ∩(xn(+*); n < ω) for every 1 ≠ x ∈ L and (ii) L is not subdirectly irreducible, is constructed. The construction is purely topological and the desired result is obtained via the known Priestly duality. The notion of an auxiliary regular double p-algebra is introduced and the algebras having this property are characterized.