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.

[1]  Ivo G. Rosenberg,et al.  Relations between clones and full monoids , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[2]  László Zádori.  GENERATION OF FINITE PARTITION LATTICES , 1986 .

[3]  Ivo G. Rosenberg,et al.  Some results on the centralizers of monoids in clone theory , 2002, Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic.

[4]  Reinhard Pöschel,et al.  Relational systems with trivial endomorphisms and polymorphisms , 1984 .

[5]  Ivo G. Rosenberg,et al.  On the centralizers of monoids in clone theory , 2003, 33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings..