Union soft set theory applied to ordered semigroups
The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal is introduced and the related properties are investigated. The concept of δ−exclusive set is given and the relations between uni-soft bi-ideals and δ−exclusive set are discussed. The concepts of two...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2020-06-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1656 |
| _version_ | 1819135056669573120 |
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| author | Raees Khan Asghar Khan Muhammad Uzair Khan Nasir Khan |
| author_facet | Raees Khan Asghar Khan Muhammad Uzair Khan Nasir Khan |
| author_sort | Raees Khan |
| collection | DOAJ |
| description | The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal is introduced and the related properties are investigated. The concept of δ−exclusive set is given and the relations between uni-soft bi-ideals and δ−exclusive set are discussed. The concepts of two types of prime uni-soft bi-ideals of an ordered semigroup S are given and it is proved that, a non-constant uni-soft bi-ideal of S is prime in the second sense if and only if each of its proper δ−exclusive set is a prime bi-ideal of S. The characterizations of left and right simple ordered semigroups are considered. Using the notion of uni-soft bi-ideals, some semilattices of left and right simple semigroups are provided. By using the properties of uni-soft bi-ideals, the characterization of a regular ordered semigroup is provided. In the last section of this paper, the characterizations of both regular and intra-regular ordered semigroups are provided. |
| first_indexed | 2024-12-22T10:13:01Z |
| format | Article |
| id | doaj.art-a10d2d9300f84274a81e91510adead70 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-22T10:13:01Z |
| publishDate | 2020-06-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-a10d2d9300f84274a81e91510adead702022-12-21T18:29:48ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392020-06-01185819837481Union soft set theory applied to ordered semigroupsRaees Khan0Asghar Khan1Muhammad Uzair KhanNasir Khan2Bacha Khan University, Charsadda, KPK PakistanAbdul Wali Khan University Mardan, KPK, PakistanGyeongsang National University, Chinju 660-701, KoreaThe uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal is introduced and the related properties are investigated. The concept of δ−exclusive set is given and the relations between uni-soft bi-ideals and δ−exclusive set are discussed. The concepts of two types of prime uni-soft bi-ideals of an ordered semigroup S are given and it is proved that, a non-constant uni-soft bi-ideal of S is prime in the second sense if and only if each of its proper δ−exclusive set is a prime bi-ideal of S. The characterizations of left and right simple ordered semigroups are considered. Using the notion of uni-soft bi-ideals, some semilattices of left and right simple semigroups are provided. By using the properties of uni-soft bi-ideals, the characterization of a regular ordered semigroup is provided. In the last section of this paper, the characterizations of both regular and intra-regular ordered semigroups are provided.http://etamaths.com/index.php/ijaa/article/view/1656 |
| spellingShingle | Raees Khan Asghar Khan Muhammad Uzair Khan Nasir Khan Union soft set theory applied to ordered semigroups International Journal of Analysis and Applications |
| title | Union soft set theory applied to ordered semigroups |
| title_full | Union soft set theory applied to ordered semigroups |
| title_fullStr | Union soft set theory applied to ordered semigroups |
| title_full_unstemmed | Union soft set theory applied to ordered semigroups |
| title_short | Union soft set theory applied to ordered semigroups |
| title_sort | union soft set theory applied to ordered semigroups |
| url | http://etamaths.com/index.php/ijaa/article/view/1656 |
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