Geodesic
A Lemma on Projective Geometries as Modular and/or Arguesian Lattices
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 283-290

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DOI

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.
DOI : 10.4153/CMB-1983-046-1
Mots-clés : 06C05, 51A05 
Day, Alan. A Lemma on Projective Geometries as Modular and/or Arguesian Lattices. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 283-290. doi: 10.4153/CMB-1983-046-1
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     title = {A {Lemma} on {Projective} {Geometries} as {Modular} and/or {Arguesian} {Lattices}},
     journal = {Canadian mathematical bulletin},
     pages = {283--290},
     year = {1983},
     volume = {26},
     number = {3},
     doi = {10.4153/CMB-1983-046-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-046-1/}
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