Relative Ockham lattices: their order-theoretic and algebraic characterisation

Bordalo, G. ; Priestley, H. A.

Glasgow mathematical journal, Tome 32 (1990) no. 1, pp. 47-66

Résumé

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.

Détail

DOI : 10.1017/S0017089500009058

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