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Algebra and Discrete Mathematics, 2004, Issue 4, Pages 1–11
(Mi adm356)
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This article is cited in 5 scientific papers (total in 5 papers)
RESEARCH ARTICLE
Clones of full terms
Klaus Deneckea, Prakit Jampachonb a University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
b KhonKaen University, Department of Mathematics, KhonKaen, 40002 Thailand
Abstract:
In this paper the well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied in a restricted setting, that of $n$-ary full hyperidentities and identities of the $n$-ary clone of term operations which are induced by full terms. We prove that the $n$-ary full terms form an algebraic structure which is called a Menger algebra of rank $n$. For a variety $V$, the set $Id_n^FV$ of all its identities built up by full $n$-ary terms forms a congruence relation on that Menger algebra. If $Id_n^FV$ is closed under all full hypersubstitutions, then the variety $V$ is called $n-F$-solid. We will give a characterization of such varieties and apply the results to $2-F$-solid varieties of commutative groupoids.
Keywords:
Clone, unitary Menger algebra of type $\tau_n$, full hyperidentity, $n-F$-solid variety.
Received: 23.02.2004 Revised: 17.12.2004
Citation:
Klaus Denecke, Prakit Jampachon, “Clones of full terms”, Algebra Discrete Math., 2004, no. 4, 1–11
Linking options:
https://www.mathnet.ru/eng/adm356 https://www.mathnet.ru/eng/adm/y2004/i4/p1
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