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 |
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| Date: | 2004 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| 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| 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.
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| ISSN: | 1726-3255 |