A Study on Groupoids, Ideals and Congruences via Cubic Sets
The inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various properties. In particula...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/9/443 |
| _version_ | 1797491228489547776 |
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| author | Jeong-Gon Lee Samy M. Mostafa Jong-Il Baek Sang-Hyeon Han Kul Hur |
| author_facet | Jeong-Gon Lee Samy M. Mostafa Jong-Il Baek Sang-Hyeon Han Kul Hur |
| author_sort | Jeong-Gon Lee |
| collection | DOAJ |
| description | The inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various properties. In particular, we give a relationship between the set of all cubic normal subgroups of a group and all cubic congruences on the group. |
| first_indexed | 2024-03-10T00:44:26Z |
| format | Article |
| id | doaj.art-c086ff6e12ea4acf9a3ad261676a2c9d |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T00:44:26Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-c086ff6e12ea4acf9a3ad261676a2c9d2023-11-23T15:02:06ZengMDPI AGAxioms2075-16802022-08-0111944310.3390/axioms11090443A Study on Groupoids, Ideals and Congruences via Cubic SetsJeong-Gon Lee0Samy M. Mostafa1Jong-Il Baek2Sang-Hyeon Han3Kul Hur4Division of Applied Mathematics, Wonkwang University, 460 Iksan-daero, Iksan-si 54538, KoreaDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11566, EgyptSchool of Big Data and Financial Statistics, Wonkwang University, 460 Iksan-daero, Iksan-si 54538, KoreaDivision of Applied Mathematics, Wonkwang University, 460 Iksan-daero, Iksan-si 54538, KoreaDivision of Applied Mathematics, Wonkwang University, 460 Iksan-daero, Iksan-si 54538, KoreaThe inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various properties. In particular, we give a relationship between the set of all cubic normal subgroups of a group and all cubic congruences on the group.https://www.mdpi.com/2075-1680/11/9/443cubic setcubic subgroupoidcubic ideal\({\widetilde{\widetilde{a}}}\)-level setcubic subgroupcubic normal subgroup |
| spellingShingle | Jeong-Gon Lee Samy M. Mostafa Jong-Il Baek Sang-Hyeon Han Kul Hur A Study on Groupoids, Ideals and Congruences via Cubic Sets Axioms cubic set cubic subgroupoid cubic ideal \({\widetilde{\widetilde{a}}}\)-level set cubic subgroup cubic normal subgroup |
| title | A Study on Groupoids, Ideals and Congruences via Cubic Sets |
| title_full | A Study on Groupoids, Ideals and Congruences via Cubic Sets |
| title_fullStr | A Study on Groupoids, Ideals and Congruences via Cubic Sets |
| title_full_unstemmed | A Study on Groupoids, Ideals and Congruences via Cubic Sets |
| title_short | A Study on Groupoids, Ideals and Congruences via Cubic Sets |
| title_sort | study on groupoids ideals and congruences via cubic sets |
| topic | cubic set cubic subgroupoid cubic ideal \({\widetilde{\widetilde{a}}}\)-level set cubic subgroup cubic normal subgroup |
| url | https://www.mdpi.com/2075-1680/11/9/443 |
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