Abstract
Finite demi-p-lattices are described in terms of the poset of its join irreducible elements endowed with a suitable set of maps. Description of the free algebras of demi-p-lattices and almost-p-lattices with n free generators are given.
Similar content being viewed by others
References
Berman, J. and P. H. Dwinger, 1975, ‘Finitely generated pseudocomplemented distributive lattices’, J. austral. Math. Soc. 19, 238–246.
Berman, J., 1977, ‘Distributive lattices wiht an additional unary operation’, Aequationes Mathematicae 16, 165–171.
Gaitán, H., ‘Free almost-p-lattices’. To appear in Czechoslovak Math. Journal.
Grätzer, G., Lattice theory; first concepts and distributive lattices, W, H. Freeman, San Francisco California.
Priestley, H. A., 1970, ‘Representation of distributive lattices by means of ordered Stone spaces’, Bull. London Math. Soc. 2, 186–190.
Priestley, H. A., 1974, ‘Stone lattices: a topological approach’, Fund. Math. 84, 127–143.
Priestley, H. A., 1975, ‘The construction of spaces dual to pseudocomplemented distributive lattices’, Quart. J. Math. Oxford 26, 215–228.
Sankappanavar, H. P., 1987, ‘Semi-De Morgan algebras’, The J. of Symbolic Logic 52, 712–724.
Sankappanavar, H. P., 1990, ‘Demi-pseudocomplemented lattices: principal congruences and subdirect irreducibility’, Algebra Universalis 27, 180–193.
Sankappanavar, H. P., 1991, ‘Varieties of demi-pseudocomplemented lattices’, Zeitsch. f. Math. Logik und Grundlagen d. Math. 37, 411–420.
Urquhart, A., 1979, ‘Distributive lattices with a dual homomorphic operation’, Studia Logica 38, 201–209.
Author information
Authors and Affiliations
Additional information
Research supported by the CDCHT (project C-602-93) of the Universidad de los Andes, Mérida, Venezuela.
Editors' Note: Demi-p-lattices are semi-deMorgan algebras, the topic of D. Hobby's contribution to this special edition. H. Gaitan's results were obtained independently.
Rights and permissions
About this article
Cite this article
Gaitan, H. Representation of finite demi-p-lattices by means of posets. Stud Logica 56, 97–110 (1996). https://doi.org/10.1007/BF00370142
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00370142