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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| Дата: | 2004 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156591 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
irk-123456789-156591 |
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irk-123456789-1565912019-06-19T01:26:10Z Clones of full terms Denecke, K. Jampachon, P. 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. 2004 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156591 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Denecke, K. Jampachon, P. |
| spellingShingle |
Denecke, K. Jampachon, P. Clones of full terms Algebra and Discrete Mathematics |
| author_facet |
Denecke, K. Jampachon, P. |
| author_sort |
Denecke, K. |
| title |
Clones of full terms |
| title_short |
Clones of full terms |
| title_full |
Clones of full terms |
| title_fullStr |
Clones of full terms |
| title_full_unstemmed |
Clones of full terms |
| title_sort |
clones of full terms |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156591 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT deneckek clonesoffullterms AT jampachonp clonesoffullterms |
| first_indexed |
2023-05-20T17:49:46Z |
| last_indexed |
2023-05-20T17:49:46Z |
| _version_ |
1796154193577246720 |