Median algebras, Relation algebras, C-algebras

  • Piergiulio Corsini
  • Violeta Leoreanu
Part of the Advances in Mathematics book series (ADMA, volume 5)


  • For the first time, median algebras appeared in the late fourties. A.A. Grau [148] characterized Boolean algebras in terms of median operation and complementation, G. Birkhoff and S.A. Kiss [25] discusses the median operation for distributive lattices. The concept of abstract median algebra was introduced by S.P. Avann [12] and later M. Scholander [356], [357], [358] and S.P. Avann [13] performed a detailed study of median algebras. More recently, J. Nieminen [301], E. Evans [139], H.M. Mulder A. Schrijver [297], J.R. Isbell [165], H. Werner [424] worked on this subject.

  • We shall see that quasi-canonical hypergroups can be characterized as the atomic structures of complete atomic integral relation algebras (§2). Moreover, the Tarski complex- algebra construction gives a fulI embedding of quasi-canonical hypergroups into relation algebras. Therefore, certain combinatorial properties of quasi-canonical hypergroups transfer to relation aI gebras. Using this process, results of Monk [295], [296] or McKenzie [263], [453], about relation algebras (or cylindric algebras) turn out to be just interpretations of quasi-canonical hypergroup results.

  • Let us remember some remarkable C-algebras: the adjancency algebras of association schemes [441], Salgebras over finite groups [31], and centralizer algebras of homogeneous coherent configurations [449].


Boolean Algebra Distributive Lattice Relation Algebra Association Scheme Combinatorial Property 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Piergiulio Corsini
    • 1
  • Violeta Leoreanu
    • 2
  1. 1.Department of Mathematics and Computer SciencesUniversity of UdineUdineItaly
  2. 2.Faculty of Mathematics“AI.I Cuza” UniversityIaşiRomania

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