On ockham algebras: Congruence lattices and subdirectly irreducible algebras

Studia Logica 55 (2):319 - 346 (1995)

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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DOI 10.1007/BF01061240
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An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
On the Representation of Quasi-Boolean Algebras.A. Bialynicki-Birula & H. Rasiowa - 1957 - Journal of Symbolic Logic 22 (4):370-370.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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