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This article is cited in 2 scientific papers (total in 2 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm1433https://doi.org/10.4213/mzm1433 https://www.mathnet.ru/eng/mzm/v64/i4/p584
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Abstract page: | 432 | Full-text PDF : | 239 | References: | 41 | First page: | 3 |
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