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Soft Computing

, Volume 12, Issue 10, pp 1027–1034 | Cite as

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

  • Anatolij DvurečenskijEmail author
  • Flavia Ventriglia
Original Paper

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.

Keywords

Generalized pseudo effect algebra Pseudo Vitali space State Monotone σ-complete algebra Loomis–Sikorski Theorem g-Effect-tribe g-Vitali space 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Slovak Academy of SciencesMathematical InstituteBratislavaSlovakia
  2. 2.Dipartimento di matematica e applicazioni, “R. Caccioppoli”Universitá degli studi di Napoli “Federico II” complesso universitarioNaplesItaly

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