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On the structure and representation of clones. (English) Zbl 0636.08003

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.
Reviewer: A.A.L.Sangalli

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras
08A35 Automorphisms and endomorphisms of algebraic structures
08A05 Structure theory of algebraic structures
08A60 Unary algebras
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References:

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