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    Arguesian lattices of order 3

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    PickeringD1981m-1b.pdf (5.621Mb)

    Date

    1981

    Author

    Pickering, Douglas

    Degree

    Master of Science

    Discipline

    Mathematical Sciences

    Subject

    Lattice theory.

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    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]

    URI

    http://knowledgecommons.lakeheadu.ca/handle/2453/2370

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