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 ar...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| 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| _version_ | 1862627388079210496 |
|---|---|
| author | Denecke, K. Jampachon, P. |
| author_facet | Denecke, K. Jampachon, P. |
| citation_txt | Clones of full terms / K. Denecke, P. Jampachon // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 4. — С. 1–11. — Бібліогр.: 3 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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.
|
| first_indexed | 2025-12-07T13:37:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156591 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:37:52Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Denecke, K. Jampachon, P. 2019-06-18T17:30:53Z 2019-06-18T17:30:53Z 2004 Clones of full terms / K. Denecke, P. Jampachon // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 4. — С. 1–11. — Бібліогр.: 3 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 08A40, 08A60, 08A02, 20M35. https://nasplib.isofts.kiev.ua/handle/123456789/156591 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Clones of full terms Article published earlier |
| spellingShingle | Clones of full terms Denecke, K. Jampachon, P. |
| title | Clones of full terms |
| title_full | Clones of full terms |
| title_fullStr | Clones of full terms |
| title_full_unstemmed | Clones of full terms |
| title_short | Clones of full terms |
| title_sort | clones of full terms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156591 |
| work_keys_str_mv | AT deneckek clonesoffullterms AT jampachonp clonesoffullterms |