Sándor Radeleczki: Generalized transitivity and related types of n-ary relations

Equivalence relations and quasiorders (i.e., reflexive and transitive binary relations) ρ have the property that an n-ary operation f preserves ρ, if and only if each unary polynomial function obtained from f by substituting constants preserves ρ. We already proved that a wider class of n-ary relations -- called generalized quasiorders -- have the same property. As a next step we introduce the notions of an n-ary equivalence relation and of an n-ary order  relation, and we prove that n-ary equivalence relations can be constructed by using only ordinary (binary) equivalence relations. Some factor-structure constructions are also investigated.