Remarks on the classification problem for infinite-dimensional Hilbert lattices
Ronald P. Morash · Proceedings of the American Mathematical Society · 1974
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 $\beta \in D$.