Geodesic
The Gleason theorem for the field of rational numbers and residue fields
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 584-591

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Charges $\mu$ 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 $\mu(P)=\operatorname{tr}(T_\mu P)$, where $T_\mu$ is a linear operator, is proved. 
@article{MZM_1998_64_4_a10,
     author = {D. Kh. Mushtari},
     title = {The {Gleason} theorem for the field of rational numbers and residue fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {584--591},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a10/}
}
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D. Kh. Mushtari. The Gleason theorem for the field of rational numbers and residue fields. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 584-591. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a10/