Algebras assigned to ternary relations
Ivan Chajda, Miroslav Kolařík, Helmut Länger · Miskolc mathematical notes/Mathematical notes · 2013
We show that to every centred ternary relation T on a set A there can be assigned (in a non-unique way) a ternary operation t on A such that the identities satisfied by .AI t/ reflect relational properties of T .We classify ternary operations assigned to centred ternary relations and we show how the concepts of relational subsystems and homomorphisms are connected with subalgebras and homomorphisms of the assigned algebra .AI t/.We show that for ternary relations having a non-void median can be derived so-called median-like algebras .AI t/ which become median algebras if the median M T .a;b; c/ is a singleton for all a; b; c 2 A. Finally, we introduce certain algebras assigned to cyclically ordered sets.