Some results on the centralizers of monoids in clone theory

For a set S of multi-variable operations on a k-element set, the centralizer S´ is the set of operations which commute with all operations in S. In this paper we concentrate on monoids of unary operations and centralizers of such monoids. In the course of discussion the Kuznetsov criterion is effectively used. First we study such monoids whose centralizer is the trivial (least) clone J_k. Next we prove that the trivial monoid {id} is the only monoid whose centralizer is the clone of all operations. We also show that the centralizer of every (non-trivial) monoid is included in maximal clones of some specific kinds