Abundant semigroups with medial idempotents
The effect of the existence of a medial or related idempotent in any abundant semigroup is the subject of this paper. The aim is to naturally order any abundant semigroup $S$ which contains an ample multiplicative medial idempotent $u$ in a way that $\mathcal{L}^*$ and $\mathcal{R}^*$ are compatible...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2021-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_87496_a4ebaaabf0e12fcab41f427e46088cd3.pdf |
| _version_ | 1818606931356418048 |
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| author | Abdulsalam El-Qallali |
| author_facet | Abdulsalam El-Qallali |
| author_sort | Abdulsalam El-Qallali |
| collection | DOAJ |
| description | The effect of the existence of a medial or related idempotent in any abundant semigroup is the subject of this paper. The aim is to naturally order any abundant semigroup $S$ which contains an ample multiplicative medial idempotent $u$ in a way that $\mathcal{L}^*$ and $\mathcal{R}^*$ are compatible with the natural order and $u$ is a maximum idempotent. The structure of an abundant semigroup containing an ample normal medial idempotent studied in \cite{item6} will be revisited. |
| first_indexed | 2024-12-16T14:18:42Z |
| format | Article |
| id | doaj.art-63a9b374865d4f5ca3298f3216479d86 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-16T14:18:42Z |
| publishDate | 2021-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-63a9b374865d4f5ca3298f3216479d862022-12-21T22:28:34ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612021-07-0115113410.52547/cgasa.15.1.187496Abundant semigroups with medial idempotentsAbdulsalam El-Qallali0Department of Mathematics, Faculty of Science, University of Tripoli, Tripoli, LibyaThe effect of the existence of a medial or related idempotent in any abundant semigroup is the subject of this paper. The aim is to naturally order any abundant semigroup $S$ which contains an ample multiplicative medial idempotent $u$ in a way that $\mathcal{L}^*$ and $\mathcal{R}^*$ are compatible with the natural order and $u$ is a maximum idempotent. The structure of an abundant semigroup containing an ample normal medial idempotent studied in \cite{item6} will be revisited.https://cgasa.sbu.ac.ir/article_87496_a4ebaaabf0e12fcab41f427e46088cd3.pdfabundant semigroupsample semigroupsmedial idempotentsnaturally ordered semigroups |
| spellingShingle | Abdulsalam El-Qallali Abundant semigroups with medial idempotents Categories and General Algebraic Structures with Applications abundant semigroups ample semigroups medial idempotents naturally ordered semigroups |
| title | Abundant semigroups with medial idempotents |
| title_full | Abundant semigroups with medial idempotents |
| title_fullStr | Abundant semigroups with medial idempotents |
| title_full_unstemmed | Abundant semigroups with medial idempotents |
| title_short | Abundant semigroups with medial idempotents |
| title_sort | abundant semigroups with medial idempotents |
| topic | abundant semigroups ample semigroups medial idempotents naturally ordered semigroups |
| url | https://cgasa.sbu.ac.ir/article_87496_a4ebaaabf0e12fcab41f427e46088cd3.pdf |
| work_keys_str_mv | AT abdulsalamelqallali abundantsemigroupswithmedialidempotents |