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 |
| Summary: | 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. |
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| ISSN: | 2345-5853 2345-5861 |