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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remarks on the classification problem for infinite-dimensional Hilbert lattices
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by Ronald P. Morash PDF
Proc. Amer. Math. Soc. 43 (1974), 42-46 Request permission

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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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