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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

Information

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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