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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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156591 |
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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. |
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