Sharply Orthocomplete Effect Algebras

M. Kalina, J. Paseka, Z. Riečanová

Abstract


Special types of effect algebras E called sharply dominating and S-dominating were introduced by S. Gudder in [7, 8]. 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.

Keywords


effect algebra; sharp element; central element; block; sharply dominating; S-dominating; sharply orthocomplete

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague