Type-Decomposition of an Effect Algebra |
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Authors: | David J Foulis Sylvia Pulmannová |
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Institution: | 1. Department of Mathematics and Statistics, University of Massachusetts, 1 Sutton Court, Amherst, MA, 01002, USA 2. Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73, Bratislava, Slovakia
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Abstract: | Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras. We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice. |
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