Relative Ockham lattices: their order-theoretic and algebraic characterisation
Gabriela Bordalo, Hilary A. Priestley · Glasgow Mathematical Journal · 1990
Given a variety of lattice-ordered algebras, a lattice L is said to be a relative -lattice if every closed interval [a, b] of L may be given the structure of an algebra in (in other words, is the reduct of a member of —not necessarily unique). This paper discusses the characterisation in terms of forbidden substructures of finite relative.stf-lattices. We treat a large class of varieties of distributive-lattice-ordered algebras. For these varieties, the finite algebras can be described dually in terms of finite ordered sets, so that order-theoretic results and techniques prove valuable.