This article is cited in 6 papers

Algebraically equivalent clones

A. G. Pinus

Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630092 Russia

Abstract: 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.

Keywords: clone, equationally additive clone, algebraically equivalent clones, lattice.

UDC: 512.57

Received: 02.03.2016

DOI: 10.17377/alglog.2016.55.605

 English version: Algebra and Logic, 2017, 55:6, 501–506

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