\(F\)–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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Бібліографічні деталі
Дата:2018
Автори: Giraldes, Emilia, Marques-Smith, Paula, Mitsch, Heinz
Формат: Стаття
Мова:English
Опубліковано: 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
id oai:ojs.admjournal.luguniv.edu.ua:article-859
record_format ojs
spelling 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
institution Algebra and Discrete Mathematics
baseUrl_str
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
work_keys_str_mv AT giraldesemilia fsemigroups
AT marquessmithpaula fsemigroups
AT mitschheinz fsemigroups
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last_indexed 2025-07-17T10:33:01Z
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