This article is cited in 6 papers

Galois theory for clones and superclones

N. A. Peryazev^a, I. K. Sharankhaev<sup>b

a</sup> Saint Petersburg Electrotechnical University "LETI"
^b Buryat State University

Abstract: We study clones (closed sets of operations that contain projections) and superclones on finite sets. According to A. I. Mal'tsev a clone may be considered as an algebra. If we replace algebra universe with a set of multioperations and add the operation of simplest equation solvability then we will obtain an algebra called a superclone. The paper establishes Galois connection between clones and superclones.

Keywords: clone, superclone, operation, multioperation, superposition.

UDC: 519.7

Received: 20.06.2015

DOI: 10.4213/dm1349

 English version: Discrete Mathematics and Applications, 2016, 26:4, 227–238

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