Congruence permutable symmetric extended De Morgan algebras (Q2508582)

An extended Ockham algebra is an algebra \((L;\wedge,\vee,f,k,0,1)\) of type \((2,2,1,1,0,0)\) where \((L;\wedge,\vee,0,1)\) is a bounded distributive lattice on which \(f\) is a dual endomorphism, \(k\) is an endomorphism, and \(f,k\) commute. Such an algebra is said to be symmetric if \(k^2\) is the identity map, and De Morgan if also \(f^2\) is the identity map. It is proved that a finite symmetric extended De Morgan algebra is congruence permutable if and only if it is a direct product of finitely many simple algebras.