On the structure and representation of clones
Let C be an abstract clone. We define an equivalence relation on C and show that C is isomorphic to the clone \(\hat C\) of all operations on the quotient set \(X_ C\) preserved by a monoid \(M_ C\) of transformations of \(X_ C\). It turns out that \(<X_ C,\hat C>\) is a countably generated free algebra and \(M_ C\) is the monoid generated by those endomorphisms which fix all but one generator. As an application we prove that all endomorphism monoids and automorphism groups of finite powers of algebras arise, up to isomorphism, from unary algebras.
scientific article; zbMATH DE number 4035897