Median algebras, Relation algebras, C-algebras
For the first time, median algebras appeared in the late fourties. A.A. Grau  characterized Boolean algebras in terms of median operation and complementation, G. Birkhoff and S.A. Kiss  discusses the median operation for distributive lattices. The concept of abstract median algebra was introduced by S.P. Avann  and later M. Scholander , ,  and S.P. Avann  performed a detailed study of median algebras. More recently, J. Nieminen , E. Evans , H.M. Mulder A. Schrijver , J.R. Isbell , H. Werner  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 ,  or McKenzie , , 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 , Salgebras over finite groups , and centralizer algebras of homogeneous coherent configurations .
KeywordsBoolean Algebra Distributive Lattice Relation Algebra Association Scheme Combinatorial Property
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