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Sibirsk. Mat. Zh., 2017 Volume 58, Number 4, Pages 828–833 (Mi smj2901)

Properties of the quasilinear clones containing creative functions

I. A. Malcevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the problem of characterizing clones on a three-element set by hyperidentities. We prove that there exists a hyperidentity separating any clone of quasilinear functions defined on the set $\{0,1,2\}$ each of them is either a selector or such that all its values belong to $\{0,1\}$ from any noncreative clone constituted by such functions incomparable with the initial clone.

Keywords: hyperidentity, quasilinear function, clone, clone identity, creative clone.

UDC: 512.57

MSC: 35R30

Received: 30.12.2016

DOI: 10.17377/smzh.2017.58.410


 English version:
Siberian Mathematical Journal, 2017, 58:4, 644–648

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© Steklov Math. Inst. of RAS, 2024