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Sharp Elements in Effect Algebras

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Abstract

We show that if for an arbitrary pair of orthogonal sharp elements of an effect algebra E its join exists and is sharp, then the set ES of all sharp elements of E is a subeffect algebra of E that is an orthomodular poset. Such effect algebras need not be sharply dominating but S-dominating. Further, we show that in every nonproper effect algebra E, ES is a subeffect algebra that is an orthomodular poset. Moreover, a general theorem for ES is proved.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 812 19, Bratislava 1, Slovak Republic

    Zdenka Riečanová

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  1. Zdenka Riečanová
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Riečanová, Z. Sharp Elements in Effect Algebras. International Journal of Theoretical Physics 40, 913–920 (2001). https://doi.org/10.1023/A:1004161923053

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