Ockham algebras arising from monoids

An Ockham algebra (L; f) is of boolean shape if its lattice reduct L is boolean and f is not the complementation. We investigate a natural construction of Ockham. algebras of boolean shape from any given monoid. Of particular interest is the question of when such algebras are subdirectly irreducible. In settling this, we obtain what is probably the first example of a subdirectly irreducible Ockham algebra that does not belong to the generalized variety K-omega. We also prove that every semigroup can be embedded in the monoid of endomorphisms of an Ockham algebra of boolean shape.