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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| Summary: | 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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| ISSN: | 2307-4108 2307-4116 |