\(F\)–semigroups
A semigroup \(S\) is called \(F\)- semigroup if there exists a group-congruence \(\rho\) on \(S\) such that every \(\rho\)-class contains a greatest element with respect to the natural partial order \(\leq_S\) of \(S\) (see [8]). This generalizes the concept of \(F\)-inverse semigroups introduced by...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/859 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-8592018-03-21T12:28:31Z \(F\)–semigroups Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz natural partial order, maximal elements, group congruence, residual, anticone 20M10 A semigroup \(S\) is called \(F\)- semigroup if there exists a group-congruence \(\rho\) on \(S\) such that every \(\rho\)-class contains a greatest element with respect to the natural partial order \(\leq_S\) of \(S\) (see [8]). This generalizes the concept of \(F\)-inverse semigroups introduced by V. Wagner [12] and investigated in [7]. Five different characterizations of general \(F\)-semigroups \(S\) are given: by means of residuals, by special principal anticones, by properties of the set of idempotents, by the maximal elements in \((S,\leq_S)\) and finally, an axiomatic one using an additional unary operation. Also \(F\)-semigroups in special classes are considered; in particular, inflations of semigroups and strong semilattices of monoids are studied. 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/859 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/859/389 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-03-21T12:28:31Z |
| collection |
OJS |
| language |
English |
| topic |
natural partial order maximal elements group congruence residual anticone 20M10 |
| spellingShingle |
natural partial order maximal elements group congruence residual anticone 20M10 Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz \(F\)–semigroups |
| topic_facet |
natural partial order maximal elements group congruence residual anticone 20M10 |
| format |
Article |
| author |
Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz |
| author_facet |
Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz |
| author_sort |
Giraldes, Emilia |
| title |
\(F\)–semigroups |
| title_short |
\(F\)–semigroups |
| title_full |
\(F\)–semigroups |
| title_fullStr |
\(F\)–semigroups |
| title_full_unstemmed |
\(F\)–semigroups |
| title_sort |
\(f\)–semigroups |
| description |
A semigroup \(S\) is called \(F\)- semigroup if there exists a group-congruence \(\rho\) on \(S\) such that every \(\rho\)-class contains a greatest element with respect to the natural partial order \(\leq_S\) of \(S\) (see [8]). This generalizes the concept of \(F\)-inverse semigroups introduced by V. Wagner [12] and investigated in [7]. Five different characterizations of general \(F\)-semigroups \(S\) are given: by means of residuals, by special principal anticones, by properties of the set of idempotents, by the maximal elements in \((S,\leq_S)\) and finally, an axiomatic one using an additional unary operation. Also \(F\)-semigroups in special classes are considered; in particular, inflations of semigroups and strong semilattices of monoids are studied. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/859 |
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AT giraldesemilia fsemigroups AT marquessmithpaula fsemigroups AT mitschheinz fsemigroups |
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2025-07-17T10:33:01Z |
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2025-07-17T10:33:01Z |
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