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Mat. Zametki, 1998, Volume 64, Issue 4, Pages 584–591 (Mi mz1433)  

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

D. Kh. Mushtari

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: 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.

DOI: https://doi.org/10.4213/mzm1433

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English version:
Mathematical Notes, 1998, 64:4, 506–512

Bibliographic databases:

UDC: 517.98+511.2
Received: 12.07.1996

Citation: D. Kh. Mushtari, “The Gleason theorem for the field of rational numbers and residue fields”, Mat. Zametki, 64:4 (1998), 584–591; Math. Notes, 64:4 (1998), 506–512

Citation in format AMSBIB
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