Abstract
In this paper, we study a certain class of double Ockham algebras (L; ∧, ∨, f, k, 0, 1), namely the bounded distributive lattices (L; ∧, ∨, 0, 1) endowed with a commuting pair of unary operations f and k, both of which are dual endomorphisms. We characterize the subdirectly irreducible members, and also consider the special case when both (L; f) and (L; k) are de Morgan algebras. We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.
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Fang, J. Commuting double Ockham algebras. Sci. China Ser. A-Math. 51, 185–194 (2008). https://doi.org/10.1007/s11425-007-0159-4
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DOI: https://doi.org/10.1007/s11425-007-0159-4