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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 op- erations 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.
In this paper, we study a certain class of double Ockham algebras (L; ∧, ∨, f, k, 0,1), ie bounded distributive lattices (L; ∧, ∨, 0,1) endowed with a commuting pair of unary op- erations 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.