On mappings of terms determined by hypersubstitutions
The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid. On the other hand, one can modify each hypersubstitution...
Збережено в:
| Дата: | 2005 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157195 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On mappings of terms determined by hypersubstitutions / J. Koppitz, S. Shtrakov // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 18–29. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize
all hypersubstitutions which provide bijections on the set of all
terms. The set of all such hypersubstitutions forms a monoid.
On the other hand, one can modify each hypersubstitution to
any mapping on the set of terms. For this we can consider mappings ρ from the set of all hypersubstitutions into the set of all
mappings on the set of all terms. If for each hypersubstitution σ
the application of ρ(σ) to any identity in a given variety V is again
an identity in V , so that variety is called ρ-solid. The concept of
a ρ-solid variety generalizes the concept of a solid variety. In the
present paper, we determine all ρ-solid varieties of semigroups for
particular mappings ρ. |
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