Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops
Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures m...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6649751 |
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| author | Xiaogang An Mingming Chen |
| author_facet | Xiaogang An Mingming Chen |
| author_sort | Xiaogang An |
| collection | DOAJ |
| description | Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above. We propose new notions of AG-(l,r)-Loop and AG-(r,l)-Loop, deeply study their basic properties and structural characteristics, and prove strictly the following statements: (1) each strong AG-(l,r)-Loop can be represented as the union of its disjoint sub-AG-groups, (2) the concepts of strong AG-(l,r)-Loop, strong AG-(l,l)-Loop, and AG-(l,lr)-Loop are equivalent, and (3) the concepts of strong AG-(r,l)-Loop and strong AG-(r,r)-Loop are equivalent. |
| format | Article |
| id | doaj-art-9faea0356df6492aa324dc80f3bac33a |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9faea0356df6492aa324dc80f3bac33a2025-08-20T03:38:30ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66497516649751Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet LoopsXiaogang An0Mingming Chen1School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, ChinaAbel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above. We propose new notions of AG-(l,r)-Loop and AG-(r,l)-Loop, deeply study their basic properties and structural characteristics, and prove strictly the following statements: (1) each strong AG-(l,r)-Loop can be represented as the union of its disjoint sub-AG-groups, (2) the concepts of strong AG-(l,r)-Loop, strong AG-(l,l)-Loop, and AG-(l,lr)-Loop are equivalent, and (3) the concepts of strong AG-(r,l)-Loop and strong AG-(r,r)-Loop are equivalent.http://dx.doi.org/10.1155/2021/6649751 |
| spellingShingle | Xiaogang An Mingming Chen Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops Journal of Mathematics |
| title | Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops |
| title_full | Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops |
| title_fullStr | Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops |
| title_full_unstemmed | Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops |
| title_short | Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops |
| title_sort | study of two kinds of quasi ag neutrosophic extended triplet loops |
| url | http://dx.doi.org/10.1155/2021/6649751 |
| work_keys_str_mv | AT xiaogangan studyoftwokindsofquasiagneutrosophicextendedtripletloops AT mingmingchen studyoftwokindsofquasiagneutrosophicextendedtripletloops |