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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Remarks on the classification problem for infinite-dimensional Hilbert lattices


Author: Ronald P. Morash
Journal: Proc. Amer. Math. Soc. 43 (1974), 42-46
MSC: Primary 06A30
DOI: https://doi.org/10.1090/S0002-9939-1974-0404072-4
MathSciNet review: 0404072
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Abstract: A lattice satisfying the properties of a Hilbert lattice, but possibly reducible, possesses the relative center property. The division ring with involution $ (D,\ast )$, which coordinatizes a Hilbert lattice satisfying the angle-bisection axiom and having infinite dimension, is formally real with respect to the involution, in particular having characteristic zero. Also $ D$ has the property that finite sums of elements of the form $ \alpha {\alpha ^\ast }$ are of the form $ \beta {\beta ^\ast }$ for some $ \beta \in D$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0404072-4
Keywords: Orthomodular lattice, relative center property, coordinatization, angle-bisectors
Article copyright: © Copyright 1974 American Mathematical Society