A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals
Soft set theory, introduced by Molodtsov has been considered as a successful mathematical tool for modeling uncertainties. A double-framed soft set is a generalization of a soft set, consisting of union soft sets and intersectional soft sets. An ordered AG-groupoid can be referred to as a non-associ...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2018-07-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1679 |
| _version_ | 1819135028874969088 |
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| author | Faisal Yousafzai Tauseef Asif Asghar Khan Bijan Davvaz |
| author_facet | Faisal Yousafzai Tauseef Asif Asghar Khan Bijan Davvaz |
| author_sort | Faisal Yousafzai |
| collection | DOAJ |
| description | Soft set theory, introduced by Molodtsov has been considered as a successful mathematical tool for modeling uncertainties. A double-framed soft set is a generalization of a soft set, consisting of union soft sets and intersectional soft sets. An ordered AG-groupoid can be referred to as a non-associative ordered semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest left (right) ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and double-framed soft (briefly DFS) l-ideals (r-ideals). We also give the concept of an ordered A* G**-groupoid and investigate its structural properties by using the generated ideals and DFS l-ideals (r-ideals). These concepts will verify the existing characterizations and will help in achieving more generalized results in future works. |
| first_indexed | 2024-12-22T10:12:35Z |
| format | Article |
| id | doaj.art-28985c571b084dd1882944b06b7f06a0 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-22T10:12:35Z |
| publishDate | 2018-07-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-28985c571b084dd1882944b06b7f06a02022-12-21T18:29:48ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392018-07-01164484502320A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) IdealsFaisal YousafzaiTauseef AsifAsghar KhanBijan DavvazSoft set theory, introduced by Molodtsov has been considered as a successful mathematical tool for modeling uncertainties. A double-framed soft set is a generalization of a soft set, consisting of union soft sets and intersectional soft sets. An ordered AG-groupoid can be referred to as a non-associative ordered semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest left (right) ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and double-framed soft (briefly DFS) l-ideals (r-ideals). We also give the concept of an ordered A* G**-groupoid and investigate its structural properties by using the generated ideals and DFS l-ideals (r-ideals). These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.http://etamaths.com/index.php/ijaa/article/view/1679 |
| spellingShingle | Faisal Yousafzai Tauseef Asif Asghar Khan Bijan Davvaz A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals International Journal of Analysis and Applications |
| title | A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals |
| title_full | A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals |
| title_fullStr | A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals |
| title_full_unstemmed | A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals |
| title_short | A Study of Non-Associative Ordered Semigroups in Terms of Semilattices via Smallest (Double-Framed Soft) Ideals |
| title_sort | study of non associative ordered semigroups in terms of semilattices via smallest double framed soft ideals |
| url | http://etamaths.com/index.php/ijaa/article/view/1679 |
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