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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Coordinatization of orthocomplemented and orthomodular posets


Authors: S. P. Gudder and R. H. Schelp
Journal: Proc. Amer. Math. Soc. 25 (1970), 229-237
MSC: Primary 06.35
MathSciNet review: 0258690
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0258690-3
PII: S 0002-9939(1970)0258690-3
Keywords: Partially ordered sets, orthocomplemented posets, orthomodular posets, Baer $ ^{\ast}$-semigroups, coordinatization theorems
Article copyright: © Copyright 1970 American Mathematical Society