\(F\)–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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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
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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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Algebra and Discrete Mathematics| _version_ | 1856543275173806080 |
|---|---|
| author | Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz |
| author_facet | Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz |
| author_sort | Giraldes, Emilia |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T12:28:31Z |
| 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. |
| first_indexed | 2025-12-02T15:33:01Z |
| format | Article |
| id | admjournalluguniveduua-article-859 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:33:01Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | natural partial order maximal elements group congruence residual anticone 20M10 Giraldes, Emilia Marques-Smith, Paula Mitsch, Heinz \(F\)–semigroups |
| title | \(F\)–semigroups |
| title_full | \(F\)–semigroups |
| title_fullStr | \(F\)–semigroups |
| title_full_unstemmed | \(F\)–semigroups |
| title_short | \(F\)–semigroups |
| title_sort | \(f\)–semigroups |
| topic | natural partial order maximal elements group congruence residual anticone 20M10 |
| topic_facet | natural partial order maximal elements group congruence residual anticone 20M10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/859 |
| work_keys_str_mv | AT giraldesemilia fsemigroups AT marquessmithpaula fsemigroups AT mitschheinz fsemigroups |