Geodesic
The Gleason theorem for the field of rational numbers and residue fields
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 584-591 
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/
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     title = {The {Gleason} theorem for the field of rational numbers and residue fields},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Gleason A. M., “Measures on the closed subspaces of a Hilbert space”, J. Math. Mech., 6:6 (1957), 885–893 | MR | Zbl

[2] Sherstnev A. N., “Ponyatie zaryada v nekommutativnoi skheme teorii mery”, Veroyatnostnye metody i kibernetika, no. 10–11, Kazan, 1974, 68–72 | Zbl

[3] Dorofeev S. V., Sherstnev A. N., “Funktsii repernogo vida i ikh primeneniya”, Izv. vuzov. Matem., 1990, no. 4, 23–29 | MR | Zbl

[4] Mushtari D. Kh., “Logiki proektorov v banakhovykh prostranstvakh”, Izv. vuzov. Matem., 1989, no. 8, 44–52 | MR