Commuting Hyperoperations

摘要

Centralizer of a set of hyperoperations F is a clone of hyperoperations that commute with all hyperoperations from F. There are several ways to define this commuting operator which imply several definitions of centralizers of sets of hyperoperations and they are considered in this paper. In order to obtain their properties, we discuss the definition of graph of hyperoperation, relation on A^n × (P(A) {0}) and lifting of such relation to (P(A) {0}^n+1.