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Isomorphism of Clones
Dietmar Schweigert and Rainer Lenz

A clone on a universe A is a set of functions on A containing the projections and being closed under superposition of functions. In this paper we discuss the relationship between clone isomorphism and isomorphism of general algebras. Since clone isomorphisms have to commute with the five Maltsev operations, it is difficult to decide whether between two given clones there exists an isomorphism. Dealing with this problem we use the concept of inner isomorphism of clones. Further, the isomorphism of the dual relation algebras is formulated. The inner isomorphisms induce some symmetries of the lattice LA of all clones of functions on A. We give a necessary and sufficient condition for the inner isomorphism between clones via general algebras. Moreover, approaches to clone isomorphism like the clone equivalence and the weak isomorphism of algebras are discussed.

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