F–semigroups
A semigroup S is called F- semigroup if there exists a group-congruence ρ on S such that every ρ-class contains a greatest element with respect to the natural partial order ≤S of S (see [8]). This generalizes the concept of F-inverse semigroups introduced by V. Wagner [12] and investigated in [7]. F...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2007 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152363 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | F–semigroups / E. Giraldes, P. Marques-Smith, H. Mitsch // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 67–85. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735043874521088 |
|---|---|
| author | Giraldes, E. Marques-Smith, P. Mitsch, H. |
| author_facet | Giraldes, E. Marques-Smith, P. Mitsch, H. |
| citation_txt | F–semigroups / E. Giraldes, P. Marques-Smith, H. Mitsch // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 67–85. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A semigroup S is called F- semigroup if there exists a group-congruence ρ on S such that every ρ-class contains a greatest element with respect to the natural partial order ≤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,≤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.
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| first_indexed | 2025-12-07T19:46:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152363 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:46:29Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Giraldes, E. Marques-Smith, P. Mitsch, H. 2019-06-10T14:35:05Z 2019-06-10T14:35:05Z 2007 F–semigroups / E. Giraldes, P. Marques-Smith, H. Mitsch // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 67–85. — Бібліогр.: 12 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/152363 2000 Mathematics Subject Classification:20M10. A semigroup S is called F- semigroup if there exists a group-congruence ρ on S such that every ρ-class contains a greatest element with respect to the natural partial order ≤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,≤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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics F–semigroups Article published earlier |
| spellingShingle | F–semigroups Giraldes, E. Marques-Smith, P. Mitsch, H. |
| title | F–semigroups |
| title_full | F–semigroups |
| title_fullStr | F–semigroups |
| title_full_unstemmed | F–semigroups |
| title_short | F–semigroups |
| title_sort | f–semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152363 |
| work_keys_str_mv | AT giraldese fsemigroups AT marquessmithp fsemigroups AT mitschh fsemigroups |