Coordinatization of orthocomplemented and orthomodular posets
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- by S. P. Gudder and R. H. Schelp
- Proc. Amer. Math. Soc. 25 (1970), 229-237
- DOI: https://doi.org/10.1090/S0002-9939-1970-0258690-3
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Abstract:
Generalizations of Baer $^{\ast }$-semigroups called partial Baer $^{\ast }$-semigroups and OM-partial Baer $^{\ast }$-semigroups are introduced. It is shown that the set of closed projections of a (OM) partial Baer $^{\ast }$-semigroup form an (orthomodular) orthocomplemented poset. Conversely (orthomodular) orthocomplemented posets are coordinatized by (OM) partial Baer $^{\ast }$-semigroups. It is shown that these coordinatizing semigroups are minimal.References
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- Stanley Gudder, Axiomatic quantum mechanics and generalized probability theory, Probabilistic Methods in Applied Mathematics, Vol. 2, Academic Press, New York, 1970, pp. 53–129. MR 0266552
- V. S. Varadarajan, Probability in physics and a theorem on simultaneous observability, Comm. Pure Appl. Math. 15 (1962), 189–217. MR 163616, DOI 10.1002/cpa.3160150207
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 229-237
- MSC: Primary 06.35
- DOI: https://doi.org/10.1090/S0002-9939-1970-0258690-3
- MathSciNet review: 0258690