Relative Ockham algebras
T. S. Blyth, J C Varlet · 1994
Abstract In Chapter 1 we gave an affirmative answer to the question of whether every bounded distributive lattice L can be made into an Ockham algebra (L; ∼). If the subvariety V of O to which (L; ∼) has to belong is prescribed, then the answer is far from being affirmative, even when L is finite. For example, as we observed in [41], the 5-element distributive lattice with Hasse diagram [ufig] cannot be made into an M1-algebra since otherwise we would have [ueq] whence either ∼a= l or ∼b = l, so that either ∼2a = 0 or ∼2b = 0 from which it follows by axiom (1) that either a = 0 or b = 0, a contradiction.