Arguesian lattices of order 3

Abstract

Since the mid 19th century it has been known that every Desarguean projective’ plane is coordinatizable over a division ring. This coordinatization procedure was used by von Neumann [9] to show that every complemented modular lattice with spanning n-frame (n >= 4) is isomorphic to the lattice of finitely generated submodules of a regular ring. In 1958, Jonsson introduced the Arguesian identity and extended von Neumann’s result to every complemented Arguesian lattice with spanning 3-frame. It was further noted by Freese [s] and Artmann [l] that to obtain the ring, von Neumann’s proof did not require complementation., In this thesis we follow the method of von.Neumann to show: [see thesis for theorum]