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Semigroups Co-Ordinatizing Orthomodular Geometries

Published online by Cambridge University Press:  20 November 2018

D. J. Foulis
D. J. Foulis*
Affiliation:
Wayne State University and the University of Florida
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In (2, 3, 4, and 5), the author has established a connection between orthomodular lattices and Baer *-semigroups. In brief, the connection is as follows. The lattice of closed projections of any Baer *-semigroup forms an orthomodular lattice. Conversely, if L is any orthomodular lattice, there exists a Baer *-semigroup S which co-ordinatizes L in the sense that L is isomorphic to the lattice of closed projections in S. In this note we shall assume that the reader is familiar with the results and the notation of the quoted papers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 40 - 51
Copyright
Copyright © Canadian Mathematical Society 1965

References

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