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A Lemma on Projective Geometries as Modular and/or Arguesian Lattices

Published online by Cambridge University Press:  20 November 2018

Alan Day
Alan Day*
Affiliation:
Lakehead University Thunder Bay, Ontario
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Abstract

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A projective geometry of dimension (n - 1) can be defined as modular lattice with a spanning n-diamond of atoms (i.e.: n + 1 atoms in general position whose join is the unit of the lattice). The lemma we show is that one could equivalently define a projective geometry as a modular lattice with a spanning n-diamond that is (a) is generated (qua lattice) by this n-diamond and a coordinating diagonal and (b) every non-zero member of this coordinatizing diagonal is invertible. The lemma is applied to describe certain freely generated modular and Arguesian lattices.

Keywords

06C0551A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 283 - 290
Copyright
Copyright © Canadian Mathematical Society 1983

References

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