Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0404072
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\beta \in D$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A30

Retrieve articles in all journals with MSC: 06A30

Additional Information

Keywords: Orthomodular lattice, relative center property, coordinatization, angle-bisectors
Article copyright: © Copyright 1974 American Mathematical Society