Advanced search
Publication Cover
International Journal of General Systems Volume 40, 2011 - Issue 1: Fuzzy and Quantum Systems
Submit an article Journal homepage
48
Views
1
CrossRef citations to date
0
Altmetric
Articles

Representations of pseudo Vitali spaces and Loomis–Sikorski theorem

A. Dvurečenskij Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73, Bratislava, SlovakiaCorrespondence[email protected]
&
F. Ventriglia Department of Mathematics and Applications (‘R. Caccioppoli’), University of Naples (‘Federico II’), Complex Monte S. Angelo, Via Cintia, I-801 26, Naples, ItalyView further author information
Pages 39-59 | Received 15 Oct 2008, Accepted 25 Apr 2009, Published online: 21 Jul 2010

References

  • Bosbach , B. 1982 . Concerning cone algebras . Algebra universalis , 15 : 58 – 66 .
  • Chang , C.C. 1958 . Algebraic analysis of many valued logics . Transactions of the American mathematical society , 88 : 467 – 490 .
  • Di Nola , A. , Dvurečenskij , A. , Hyčko , M. and Manara , C. 2005 . Entropy on effect algebras with the Riesz decomposition property II: MV-algebras . Kybernetika , 41 : 151 – 176 .
  • Dvurečenskij , A. 2000 . Loomis–Sikorski theorem for σ-complete MV-algebras and ℓ-groups . Journal of the Australian mathematical society series A , 68 : 261 – 277 .
  • Dvurečenskij , A. 2001 . States on pseudo MV-algebras . Studia logica , 68 : 301 – 327 .
  • Dvurečenskij , A. 2002 . Pseudo MV-algebras are intervals in ℓ-groups . Journal of the Australian mathematical society , 72 : 427 – 445 .
  • Dvurečenskij , A. and Pulmannová , S. 2000 . New trends in quantum structures , Dordrecht : Kluwer Academic Publishers . Bratislava: Ister Science
  • Dvurečenskij , A. and Vetterlein , T. 2001a . Pseudoeffect algebras. I. Basic properties . International journal of theoretical physics , 40 : 685 – 701 .
  • Dvurečenskij , A. and Vetterlein , T. 2001b . Pseudoeffect algebras. II. Group representation . International journal of theoretical physics , 40 : 703 – 726 .
  • Dvurečenskij , A. and Vetterlein , T. 2001c . “ Generalized pseudo-effect algebras ” . In Lectures on soft computing and fuzzy logic , Edited by: Di Nola , A. and Gerla , G. 89 – 111 . Berlin : Springer-Verlag Co. . Physica-Verlag
  • Dvurečenskij , A. and Vetterlein , T. 2002 . Algebras in the positive cone of po-groups . Order , 19 : 127 – 146 .
  • Fuchs , L. 1963 . Partially ordered algebraic systems , Paris : Pergamon Press .
  • Georgescu , G. and Iorgulescu , G. 2001 . Pseudo-MV algebras . Multiple valued logic , 6 : 95 – 135 .
  • Goodearl , K.R. 1986 . Partially ordered abelian groups with interpolation , Mathematical Surveys and Monographs No. 20 Providence, RI : American Mathematical Society .
  • Mac Lane , S. 1971 . Categories for the working mathematician , Berlin : Springer-Verlag .
  • Mundici , D. 1986 . Interpretation of AF C *-algebras in Łukasiewicz sentential calculus . Journal of functional analysis , 65 : 15 – 63 .
  • Mundici , D. 1999 . Tensor products and the Loomis–Sikorski theorem for MV-algebras . Advances in applied mathematics , 22 : 227 – 248 .
  • Schmidt , K.D. 1988 . “ Minimal clans: a class of ordered partial semigroups including boolean rings and lattice-ordered groups ” . In Semigroups – theory and applications (Oberwolfach 1986) , Lecture Notes in Mathematics Vol. 1320 300 – 341 . Berlin : Springer-Verlag .
  • Wyler , O. 1966 . Clans . Compositio mathematicae , 17 : 172 – 189 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.