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]