Clones of full terms

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 prov...

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Published in:Algebra and Discrete Mathematics
Date:2004
Main Authors: Denecke, K., Jampachon, P.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2004
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/156591
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Clones of full terms / K. Denecke, P. Jampachon // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 4. — С. 1–11. — Бібліогр.: 3 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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 IdF n V of all its identities built up by full n-ary terms forms a congruence relation on that Menger algebra. If IdF n V 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.
ISSN:1726-3255