Dimension and embedding theorems for geometric lattices

  • Kantor W
  • 2


    Mendeley users who have this article in their library.
  • 51


    Citations of this article.


Let G be an n-dimensional geometric lattice. Suppose that 1 ≤ e, f ≤ n - 1, e + f ≥ n, but e and f are not both n - 1. Then, in general, there are E, F ε{lunate} G with dim E = e, dim F = f, E ∇ F = 1, and dim E ∧ F = e + f - n - 1; any exception can be embedded in an n-dimensional modular geometric lattice M in such a way that joins and dimensions agree in G and M, as do intersections of modular pairs, while each point and line of M is the intersection (in M) of the elements of G containing it. © 1974.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • William M. Kantor

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free