Products of Relations

  • Gunther Schmidt
  • Michael Winter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2208)


In Definition  2.2.1, we have introduced the direct power of a set—modelling the concept of a powerset—and shown that it is uniquely determined up to isomorphism. Even earlier, we have defined the natural projection of a set equipped with an equivalence to the set of its classes. We are now going to handle the direct product and direct sum.


  1. [BHSV94]
    Rudolf Berghammer, Armando Martín Haeberer, Gunther Schmidt, and Paulo A. S. Veloso. Comparing two different approaches to products in abstract relation algebra. In Maurice Nivat, Charles Rattray, Teodore Rus, and Giuseppe Scollo, editors, Algebraic Methodology and Software Technology, Workshops in Computing, pages 167–176. Springer-Verlag, 1994.CrossRefGoogle Scholar
  2. [Des99]
    Jules Desharnais. Monomorphic characterization of n-ary direct products. Information Sciences, 119:275–288, 1999.MathSciNetCrossRefGoogle Scholar
  3. [KS00]
    Wolfram Kahl and Gunther Schmidt. Exploring (Finite) Relation Algebras With Tools Written in Haskell. Technical Report 2000/02, Fakultät für Informatik, Universität der Bundeswehr München, October 2000., 158 pages.
  4. [Sch11a]
    Gunther Schmidt. Partiality I: Embedding Relation Algebras. Journal of Logic and Algebraic Programming, 66(2):212–238, 2006. Special issue edited by Bernhard Möller;
  5. [Sch12]
    Gunther Schmidt. Partiality II: Constructed Relation Algebras. Journal of Logic and Algebraic Programming, 81(6):660–679, 2012. Special Issue edited by Harrie de Swart,
  6. [Zie88]
    Hans Zierer. Programmierung mit Funktionsobjekten: Konstruktive Erzeugung semantischer Bereiche und Anwendung auf die partielle Auswertung. PhD thesis, Fakultät für Informatik, Technische Universität München, 1988.Google Scholar
  7. [Zie91]
    Hans Zierer. Relation algebraic domain constructions. Theoret. Comput. Sci., 87:163–188, 1991.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gunther Schmidt
    • 1
  • Michael Winter
    • 2
  1. 1.Fakultät für InformatikUniversität der Bundeswehr MünchenNeubibergGermany
  2. 2.Department of Computer ScienceBrock UniversitySt. CatharinesCanada

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