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Some embedding theorems for lattices


Hartmanis, Juris (1955) Some embedding theorems for lattices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/40KS-0T27.


In this thesis we give a general definition of a geometry on a set S and consider the lattices of the subspaces of these geometries.

First, we show that all such geometries on a fixed set S form a lattice and we investigate its properties.

Secondly, we show that the lattice of all geometries on a fixed set S is isomorphic to the lattice of subspaces of some geometry and we characterize all such geometries.

Finally, we show that every finite lattice can be embedded in the lattice of all geometries on some finite set S. This reduces the unsolved problem of embedding every finite lattice into a finite partition lattice to the problem of embedding every finite lattice of geometries into a finite partition lattice.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dilworth, Robert P.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1955
Record Number:CaltechETD:etd-12032003-102713
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4734
Deposited By: Imported from ETD-db
Deposited On:10 Dec 2003
Last Modified:21 Dec 2019 03:56

Thesis Files

PDF (Hartmanis_j_1955.pdf) - Final Version
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