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On Ockham algebras: Congruence lattices and subdirectly irreducible algebras

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Abstract

Distributive bounded lattices with a dual homomorphism as unary operation, called Ockham algebras, were firstly studied by Berman (1977). The varieties of Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras are some of the well known subvarieties of Ockham algebra. In this paper, new results about the congruence lattice of Ockham algebras are given. From these results and Urquhart's representation theorem for Ockham algebras a complete characterization of the subdirectly irreducible Ockham algebras is obtained. These results are particularized for a large number of subvarieties of Ockham algebras. For these subvarieties a full description of their subdirectly irreducible algebras is given as well.

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We are deeply grateful to Prof. H. Rasiowa for her great help during the preparation of this paper. We are also greatly indebted to L. Godo and the referees for their valuable suggestions and advices.

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Garcia, P., Esteva, F. On Ockham algebras: Congruence lattices and subdirectly irreducible algebras. Stud Logica 55, 319–346 (1995). https://doi.org/10.1007/BF01061240

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