The gleason theorem for the field of rational numbers and residue fields

Abstract

Charges μ taking values in a field F and defined on orthomodular partially ordered sets (logics) of all projectors in some finite-dimensional linear space over F are considered. In the cases where F is the field of rational numbers or a residue field, the Gleason representation μ(P) = tr(T μP), where T μ is a linear operator, is proved. © 1999 Kluwcr Academic/Plenum Publishers.