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Description of the endomorphisms of the algebra of arithmetic functions with the operations of addition and superposition. (English. Russian original) Zbl 1208.03043

Math. Notes 82, No. 6, 803-805 (2007); translation from Mat. Zametki 82, No. 6, 891-893 (2007).
Summary: In this note, a description of all endomorphisms of the algebra of one-place arithmetic functions with the operations of addition and superposition of two functions is given.

MSC:

03D20 Recursive functions and relations, subrecursive hierarchies
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References:

[1] A. I. Mal’tsev, ”Constructive algebras. I,” Uspekhi Mat. Nauk 16(3), 3–60 (1961) [in Russian].
[2] E. A. Polyakov [Poljakov], ”Some properties of algebras of recursive functions,” Algebra i Logika 3(3), 39–57 (1964).
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