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...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2005 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157195 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1726-3255 |