Abstract
The aim of this paper is to give a characterization of the (finitely) subdirectly irreducible double demi-p-lattices. First, we prove a congruence representation theorem for double demi-p-lattices, which is a natural analogue of the theorem given in [2] for double p-algebras. These results are inspired by the representation theorem given by Lakser [6] for p-algebras, and yield a natural approach to the study of subdirectly irreducible algebras.
Similar content being viewed by others
References
R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press (Columbia, Missouri, 1974).
H. Gramaglia and D. Vaggione, A note on distributive double p-algebras, preprint.
G. Grätzer, Universal Algebra, Van Nostrand (Princeton, 1979).
G. Grätzer, General Lattice Theory, Mathematische Reihe, 52, Birkhaüser Verlag, 1998.
T. Katriňák, Subdirectly irreducible distributive double p-algebras, Algebra Universalis, 10 (1980), 195–219.
H. Lakser, The structure of pseudo-complemented distributive lattices I: subdirect decomposition, Trans. Amer. Math. Soc., 156 (1971), 335–342.
H. Sankappanavar, Principal congruences of double demi-p-lattices, Algebra Universalis, 27 (1990), 248–253.
H. Sankappanavar, Semi-De Morgan algebras, J. Symbolic Logic, 52 (1987), 712–724.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gramaglia, H. Subdirectly Irreducible Double Demi-p-Lattices. Acta Mathematica Hungarica 88, 323–329 (2000). https://doi.org/10.1023/A:1026780107601
Issue Date:
DOI: https://doi.org/10.1023/A:1026780107601