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 to a...

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Date:2018
Main Authors: Koppitz, Jorg, Shtrakov, Slavcho
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-925
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-9252018-03-21T06:47:49Z On mappings of terms determined by hypersubstitutions Koppitz, Jorg Shtrakov, Slavcho \(\rho\)-solid, hypersubstitution, bijection 20M14, 20M07 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 \(\rho \) from the set of all hypersubstitutions into the set of all mappings on the set of all terms. If for each hypersubstitution \(\sigma \) the application of \(\rho (\sigma )\) to any identity  in a given variety \(V\) is again an identity in \(V\), so that variety is called \(\rho \)-solid. The concept of a \(\rho \)-solid variety generalizes the concept of a solid variety. In the present paper, we determine all \(\rho \)-solid varieties of semigroups for particular mappings \( \rho \). Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925 Algebra and Discrete Mathematics; Vol 4, No 3 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925/454 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T06:47:49Z
collection OJS
language English
topic \(\rho\)-solid
hypersubstitution
bijection
20M14
20M07
spellingShingle \(\rho\)-solid
hypersubstitution
bijection
20M14
20M07
Koppitz, Jorg
Shtrakov, Slavcho
On mappings of terms determined by hypersubstitutions
topic_facet \(\rho\)-solid
hypersubstitution
bijection
20M14
20M07
format Article
author Koppitz, Jorg
Shtrakov, Slavcho
author_facet Koppitz, Jorg
Shtrakov, Slavcho
author_sort Koppitz, Jorg
title On mappings of terms determined by hypersubstitutions
title_short On mappings of terms determined by hypersubstitutions
title_full On mappings of terms determined by hypersubstitutions
title_fullStr On mappings of terms determined by hypersubstitutions
title_full_unstemmed On mappings of terms determined by hypersubstitutions
title_sort on mappings of terms determined by hypersubstitutions
description 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 \(\rho \) from the set of all hypersubstitutions into the set of all mappings on the set of all terms. If for each hypersubstitution \(\sigma \) the application of \(\rho (\sigma )\) to any identity  in a given variety \(V\) is again an identity in \(V\), so that variety is called \(\rho \)-solid. The concept of a \(\rho \)-solid variety generalizes the concept of a solid variety. In the present paper, we determine all \(\rho \)-solid varieties of semigroups for particular mappings \( \rho \).
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925
work_keys_str_mv AT koppitzjorg onmappingsoftermsdeterminedbyhypersubstitutions
AT shtrakovslavcho onmappingsoftermsdeterminedbyhypersubstitutions
first_indexed 2025-07-17T10:34:50Z
last_indexed 2025-07-17T10:34:50Z
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