Sharply Orthocomplete Effect Algebras

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.