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Relative Ockham lattices: their order-theoretic and algebraic characterisation

Published online by Cambridge University Press:  18 May 2009

G. Bordalo  and
H. A. Priestley
G. Bordalo
Affiliation:
Faculdade de Ciencias, Departmento de Matematica, Rua Ernesto de Vasconcelos, Bloco C1, Piso 3°–, 1700 Lisboa, Portugal.
H. A. Priestley
Affiliation:
Mathematical Institute, 24–29 St. Giles, Oxford Ox1 3LB, England.
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 47 - 66
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

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