A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids),
The various generalized associative laws can be considered as generalizations of traditional symmetry. Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-grou...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of New Mexico
2020-09-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | https://fs.unm.edu/NSS/AKindofNonAssociative12.pdf |
| _version_ | 1797769001805283328 |
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| author | Xiaohong Zhang Wangtao Yuan Mingming Chen |
| author_facet | Xiaohong Zhang Wangtao Yuan Mingming Chen |
| author_sort | Xiaohong Zhang |
| collection | DOAJ |
| description | The various generalized associative laws can be considered as generalizations of traditional symmetry. Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-groupoid), and gives some examples and basic properties. Furthermore, as a combination of neutrosophic extended triplet group (NETG) and T2CA groupoid, the notion of type-2 cyclic associative neutrosophic extended triplet groupoid (T2CA NET-groupoid) is introduced, and a decomposition theorem of T2CA-NET-groupoid is proved. Finally, as a generalization of neutrosophic extended triplet group (NETG), the concept of quasi neutrosophic extended triplet groupoid (QNET-groupoid) is introduced, and the relationships among T2CA-QNET-groupoid, T2CA-NET-groupoid and CA-NET-groupoid are discussed. |
| first_indexed | 2024-03-12T21:02:31Z |
| format | Article |
| id | doaj.art-ec641b73d9cb40cbaa99673f7344f889 |
| institution | Directory Open Access Journal |
| issn | 2331-6055 2331-608X |
| language | English |
| last_indexed | 2024-03-12T21:02:31Z |
| publishDate | 2020-09-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj.art-ec641b73d9cb40cbaa99673f7344f8892023-07-31T06:32:39ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2020-09-013614416310.5281/zenodo.4065422A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), Xiaohong ZhangWangtao Yuan Mingming ChenThe various generalized associative laws can be considered as generalizations of traditional symmetry. Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-groupoid), and gives some examples and basic properties. Furthermore, as a combination of neutrosophic extended triplet group (NETG) and T2CA groupoid, the notion of type-2 cyclic associative neutrosophic extended triplet groupoid (T2CA NET-groupoid) is introduced, and a decomposition theorem of T2CA-NET-groupoid is proved. Finally, as a generalization of neutrosophic extended triplet group (NETG), the concept of quasi neutrosophic extended triplet groupoid (QNET-groupoid) is introduced, and the relationships among T2CA-QNET-groupoid, T2CA-NET-groupoid and CA-NET-groupoid are discussed.https://fs.unm.edu/NSS/AKindofNonAssociative12.pdfsemigroup; type-2 cyclic associative groupoidneutrosophic extended triplet groupdecomposition theorem |
| spellingShingle | Xiaohong Zhang Wangtao Yuan Mingming Chen A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), Neutrosophic Sets and Systems semigroup; type-2 cyclic associative groupoid neutrosophic extended triplet group decomposition theorem |
| title | A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), |
| title_full | A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), |
| title_fullStr | A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), |
| title_full_unstemmed | A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), |
| title_short | A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids), |
| title_sort | kind of non associative groupoids and quasi neutrosophic extended triplet groupoids qnet groupoids |
| topic | semigroup; type-2 cyclic associative groupoid neutrosophic extended triplet group decomposition theorem |
| url | https://fs.unm.edu/NSS/AKindofNonAssociative12.pdf |
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