A soft set theoretic approach to an AG-groupoid via ideal theory with applications
Abstract In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-12-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s42787-019-0060-7 |
| _version_ | 1818726983599652864 |
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| author | Faisal Yousafzai Mohammed M. Khalaf |
| author_facet | Faisal Yousafzai Mohammed M. Khalaf |
| author_sort | Faisal Yousafzai |
| collection | DOAJ |
| description | Abstract In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part of various problems. We also characterize a weakly regular class of an AG***-groupoid by using generated ideals and soft intersection ideals. We investigate the relationship between SI-left-ideal, SI-right-ideal, SI-two-sided-ideal, and SI-interior-ideal of an AG-groupoid over a universe set by providing some practical examples. |
| first_indexed | 2024-12-17T22:06:52Z |
| format | Article |
| id | doaj.art-77293d1c5b844a7480f68bcc7ab14e5b |
| institution | Directory Open Access Journal |
| issn | 2090-9128 |
| language | English |
| last_indexed | 2024-12-17T22:06:52Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-77293d1c5b844a7480f68bcc7ab14e5b2022-12-21T21:30:50ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282019-12-0127111810.1186/s42787-019-0060-7A soft set theoretic approach to an AG-groupoid via ideal theory with applicationsFaisal Yousafzai0Mohammed M. Khalaf1Military College of Engineering, National University of Sciences and Technology (NUST)Higher Institute of Engineering and Technology, King MarioutAbstract In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part of various problems. We also characterize a weakly regular class of an AG***-groupoid by using generated ideals and soft intersection ideals. We investigate the relationship between SI-left-ideal, SI-right-ideal, SI-two-sided-ideal, and SI-interior-ideal of an AG-groupoid over a universe set by providing some practical examples.https://doi.org/10.1186/s42787-019-0060-7Left invertive lawSoft-setsAG-groupoidRight regularityWeak regularity and SI-ideals |
| spellingShingle | Faisal Yousafzai Mohammed M. Khalaf A soft set theoretic approach to an AG-groupoid via ideal theory with applications Journal of the Egyptian Mathematical Society Left invertive law Soft-sets AG-groupoid Right regularity Weak regularity and SI-ideals |
| title | A soft set theoretic approach to an AG-groupoid via ideal theory with applications |
| title_full | A soft set theoretic approach to an AG-groupoid via ideal theory with applications |
| title_fullStr | A soft set theoretic approach to an AG-groupoid via ideal theory with applications |
| title_full_unstemmed | A soft set theoretic approach to an AG-groupoid via ideal theory with applications |
| title_short | A soft set theoretic approach to an AG-groupoid via ideal theory with applications |
| title_sort | soft set theoretic approach to an ag groupoid via ideal theory with applications |
| topic | Left invertive law Soft-sets AG-groupoid Right regularity Weak regularity and SI-ideals |
| url | https://doi.org/10.1186/s42787-019-0060-7 |
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