On left restriction semigroups with zero
In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups. Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem. We also show that every atomistic left restrictio...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Kuwait Journal of Science |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/16921 |
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| _version_ | 1849744757834645504 |
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| author | Baddi Ul Zaman |
| author_facet | Baddi Ul Zaman |
| author_sort | Baddi Ul Zaman |
| collection | DOAJ |
| description |
In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups. Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem. We also show that every atomistic left restriction semigroup S can be decomposed as an orthogonal sum of atomistic left restriction semigroups Ni , where each summand Ni is an irreducible ideal of S. Finally, properties of the summands Ni , when S embeds in some PT X the partial transformation monoid on a set X, are investigated
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| format | Article |
| id | doaj-art-1cb035be4dc3482da794e975f64c348e |
| institution | DOAJ |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-1cb035be4dc3482da794e975f64c348e2025-08-20T03:09:45ZengElsevierKuwait Journal of Science2307-41082307-41162023-03-01502A10.48129/kjs.16921On left restriction semigroups with zeroBaddi Ul Zaman0School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China In this article, we give the notion of left restriction meet-semigroup, and establish some results regarding atomistic left restriction semigroups. Then we discuss decompositions of (non-zero) semigroups with zero by proving a decomposition theorem. We also show that every atomistic left restriction semigroup S can be decomposed as an orthogonal sum of atomistic left restriction semigroups Ni , where each summand Ni is an irreducible ideal of S. Finally, properties of the summands Ni , when S embeds in some PT X the partial transformation monoid on a set X, are investigated https://journalskuwait.org/kjs/index.php/KJS/article/view/16921 |
| spellingShingle | Baddi Ul Zaman On left restriction semigroups with zero Kuwait Journal of Science |
| title | On left restriction semigroups with zero |
| title_full | On left restriction semigroups with zero |
| title_fullStr | On left restriction semigroups with zero |
| title_full_unstemmed | On left restriction semigroups with zero |
| title_short | On left restriction semigroups with zero |
| title_sort | on left restriction semigroups with zero |
| url | https://journalskuwait.org/kjs/index.php/KJS/article/view/16921 |
| work_keys_str_mv | AT baddiulzaman onleftrestrictionsemigroupswithzero |