Ockham algebras with double pseudocomplementation (Q861602)

A (universal) algebra \((L; \vee, \wedge, f, ^*, ^+, 0, 1)\) is called a double pseudocomplemented Ockham algebra (shortly, \textbf{dpO}), if \(L=(L; \vee, \wedge, 0, 1)\) is a bounded distributive lattice together with three unary operations, \(f\), \(^*\) and \(^+\), such that (i) \((L; f)\) is an Ockham algebra, (ii) \(^*\) is the operation of pseudocomplementation, (iii) \(^+\) is the operation of dual pseudocomplementation, (iv) \(f\) and \(^*\) commute and (v) \(f\) and \(^+\) commute. The author describes (i) the principal congruence relations in \textbf{dpO} and (ii) characterizes the subdirectly irreducible algebras that belong to the subvariety of \textbf{dpO} defined by the identity \(f=f^3.\)