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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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Keywords: Partially ordered sets, orthocomplemented posets, orthomodular posets, Baer $ ^{\ast}$-semigroups, coordinatization theorems
Article copyright: © Copyright 1970 American Mathematical Society

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