Two functional clones F and G on a set A are said to be algebraically equivalent if sets of solutions for F- and G-equations coincide on A. It is proved that pairwise algebraically nonequivalent existentially additive clones on finite sets A are finite in number. We come up with results on the structure of algebraic equivalence classes, including an equationally additive clone, in the lattices of all clones on finite sets.
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(A. G. Pinus) Supported by the Russian Ministry of Education and Science (gov. contract 2014/138, project No. 1052).
Translated from Algebra i Logika, Vol. 55, No. 6, pp. 760-768, November-December, 2016.
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Pinus, A.G. Algebraically Equivalent Clones. Algebra Logic 55, 501–506 (2017). https://doi.org/10.1007/s10469-017-9420-2
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DOI: https://doi.org/10.1007/s10469-017-9420-2