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arXiv · 1005.3678

Sharply Orthocomplete Effect Algebras

Martin Kalina·Jan Paseka·Zdenka Riečanová
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Abstract

Special types of effect algebras $E$ called sharply dominating and S-dominating were introduced by S. Gudder in \cite{gudder1,gudder2}. We prove statements about connections between sharp orthocompleteness, sharp dominancy and completeness of $E$. Namely we prove that in every sharply orthocomplete S-dominating effect algebra $E$ the set of sharp elements and the center of $E$ are complete lattices bifull in $E$. If an Archimedean atomic lattice effect algebra $E$ is sharply orthocomplete then it is complete.

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Martin Kalina, Jan Paseka, Zdenka Riečanová. 2010-05-20. Sharply Orthocomplete Effect Algebras. https://arxiv.org/abs/1005.3678

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