Abstract
This is the first of a planned series of papers on the structure of non-Arguesian modular lattices. Apart from the (subspace lattices of) non-Arguesian projective planes, the best known examples of such lattices are obtained via the Hall-Dilworth construction by ‘badly’ gluing together two projective planes of the same order. Our principal result shows that every non-Arguesian modular lattice L retains some of the flavor of these examples: There exist in the ideal lattice of L 20 intervals, not necessarily distinct, that form non-degenerate projective plains, and 10 points and 10 lines in these planes that constitute in a natural sense a ‘classical’ non-Arguesian configuration.
AMS (MOS) subject classifications (1980)
Primary: 06C05 secondary: 51A30Key words
Arguesian lattice perspectivity configuration projective planePreview
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© D. Reidel Publishing Company 1986