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On two versions of the Loomis–Sikorski Theorem for algebraic structures

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Abstract

We present two versions of the Loomis–Sikorski Theorem, one for monotone σ-complete generalized pseudo effect algebras with strong unit satisfying a kind of the Riesz decomposition property. The second one is for Dedekind σ-complete positive pseudo Vitali spaces with strong unit. For any case we can find an appropriate system of nonnegative bounded functions forming an algebra of the given type with the operations defined by points that maps epimorphically onto the algebra.

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Authors and Affiliations

  1. Slovak Academy of Sciences, Mathematical Institute, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Dipartimento di matematica e applicazioni, “R. Caccioppoli”, Universitá degli studi di Napoli “Federico II” complesso universitario, “Monte S. Angelo”, Via Cintia, 801 26, Naples, Italy

    Flavia Ventriglia

Authors
  1. Anatolij Dvurečenskij
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  2. Flavia Ventriglia
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Correspondence to Anatolij Dvurečenskij.

Additional information

The paper has been supported by the Center of Excellence SAS—Physics of Information—I/2/2005, the grant VEGA No. 2/6088/26 SAV, the Slovak Research and Development Agency under the contract No. APVV-0071-06, Slovak-Italian Project No. 15:“Algebraic and logical systems of soft computing”, and MURST, project “Analisi Reale”.

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Dvurečenskij, A., Ventriglia, F. On two versions of the Loomis–Sikorski Theorem for algebraic structures. Soft Comput 12, 1027–1034 (2008). https://doi.org/10.1007/s00500-007-0262-z

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