Monoids whose centralizer is the least clone

For a monoid M of k-valued unary functions, the centralizer M* is the set of k-valued multi-variable functions which commute with every function in M. In this paper, we consider the problem of finding monoids whose centralizer is the least clone. First we give a sufficient condition for M to have the least clone as its centralizer and show how it can be applied to some concrete examples of M. Then we use Zadori´s theorem to obtain another condition for M to satisfy this property.