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Published online by Cambridge University Press: 09 April 2009
Epstein and Horn, in their paper ‘Chain based lattices’, characterized P1-lattices, and P2-lattices in terms of their prime ideals. But no such prime ideal characterization for P0-lattices was given. Our main aim in this paper is to characterize P0-lattices in terms of their prime ideals. We also give a necessary and sufficient condition for a P-algebra to be a P0-lattice (and hence a P2-lattice).