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Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem

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Abstract

We prove an algebraic and a topological decomposition theorem for complete pseudo-D-lattices (i.e. lattice-ordered pseudo-effect algebras). As a consequence, we obtain a Hammer–Sobczyk type decomposition theorem for group-valued modular measures defined on pseudo-D-lattices and compactness of the range of every \(\mathbb {R}^{n} \)-valued σ-additive modular measure on a σ-complete pseudo-D-lattice.

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Authors and Affiliations

  1. Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Anna Avallone & Paolo Vitolo

  2. Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100, Udine, Italy

    Giuseppina Barbieri & Hans Weber

Authors
  1. Anna Avallone
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  2. Giuseppina Barbieri
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  3. Paolo Vitolo
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  4. Hans Weber
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Correspondence to Paolo Vitolo.

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Avallone, A., Barbieri, G., Vitolo, P. et al. Decomposition of Pseudo-effect Algebras and the Hammer–Sobczyk Theorem. Order 33, 477–501 (2016). https://doi.org/10.1007/s11083-015-9380-x

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