A structural characterization of non-Arguesian lattices

✍ Scribed by Alan Day; Bjarni Jónsson

• Publisher: Springer Netherlands
• Year: 1985
• Tongue: English
• Weight: 831 KB
• Volume: 2
• Category: Article
• ISSN: 0167-8094
• DOI: 10.1007/bf00367423

✦ Synopsis

This is the fist 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 Hal-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).