Some Centralizing Monoids on a Three-Element Set
For an algebra A on a universe A the set of endomorphisms of A forms a monoid of selfmaps on A. We call such monoids centralizing monoids. In this paper we study the first interesting case of a 3-element set A. In the lattice of inclusion-ordered centralizing monoids we find three maximal centralizing monoids. This knowledge suggests that many large monoids are not centralizing monoids.
centralizer centralizing monoid clone