Riečanová, Zdenka Distributive atomic effect algebras. (English) Zbl 1039.03050 Demonstr. Math. 36, No. 2, 247-259 (2003). It is proved that the MacNeille completion of an Archimedean atomic distributive effect algebra is a direct product of finite chains and distributive diamonds. As a consequence, for such effect algebras \(E\) it is proved: (1) every faithful or \((o)\)-continuous state on \(E\) is a valuation (hence a subadditive state); (2) there is an \((o)\)-continuous valuation on \(E\), (3) if \(E\) is complete then it is a homomorphic image of a complete atomic modular ortholattice. Reviewer: Josef Tkadlec (Praha) Cited in 10 Documents MSC: 03G12 Quantum logic 06D35 MV-algebras 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:effect algebra; MacNeille completion; valuation; MV-algebra PDFBibTeX XMLCite \textit{Z. Riečanová}, Demonstr. Math. 36, No. 2, 247--259 (2003; Zbl 1039.03050)