MMN-507
Algebras assigned to ternary relations
Ivan Chajda; Miroslav Kolařík; Helmut Länger;Abstract
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 satis¯ed by (A; t) re°ect 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
(A; t). We show that for ternary relations having a non-void median can be
derived so-called median-like algebras (A; t) which become median algebras
if the median MT (a; b; c) is a singleton for all a; b; c 2 A. Finally, we
introduce certain algebras assigned to cyclically ordered sets.
Vol. 14 (2013), No. 3, pp. 827-844
DOI: 10.18514/MMN.2013.507