Ockham algebras with De Morgan skeletons (Q1119670)

An Ockham algebra (L,f) consists of a bounded distributive lattice L and of a dual endomorphism f of L. The authors deal with the class \(K_{1,1}\) of Ockham algebras defined by \(f=f^ 3\). There are 19 non- trivial subdirectly irreducible algebras in \(K_{1,1}\) (H. Sankanappanavar and R. Beazer). The main result of the paper is the description of the lattice of all subvarieties of \(K_{1,1}\); see Section 2: this lattice has 403 elements and a rather complicated structure; an impressive result. In section 4, finite equational bases are provided for many of these varieties.