Endoprimal Monoids and Witness Lemma in Clone Theory
Hajime Machida, Ivo G. Rosenberg · 2010
For a fixed set A, an endoprimal monoid M is a set of unary functions on A which commute with some set F of functions on A. A member of such M defines an endomorphism on F. It is known to be hard to effectively characterize such endoprimal monoids. In this paper we present and discuss the ''witness lemma'' to study endoprimal monoids. Then, for the case where |A| = 3, we verify two monoids to be endoprimal and then determine all endoprimal monoids having subsets of unary functions as their witnesses.