On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids) PDF Download
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Author: Xiaohong Zhang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11
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Book Description
From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.
Author: Xiaohong Zhang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11
Get Book Here
Book Description
From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.
Author: Xiaoying Wu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied.
Author: Xiaogang An
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 20
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Book Description
A group is an algebraic system that characterizes symmetry. As a generalization of the concept of a group, semigroups and various non-associative groupoids can be considered as algebraic abstractions of generalized symmetry.
Author: Xiaogang An
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book 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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 353
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Book Description
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra, Neutrosophic Triplet Partial Bipolar Metric Spaces, The Neutrosophic Triplet of BI-algebras.
Author: Yingcang Ma
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16
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Book Description
Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 341
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Book Description
Contributors to current issue (listed in papers’ order): Atena Tahmasbpour Meikola, Arif Mehmood, Wadood Ullah, Said Broumi, Muhammad Imran Khan, Humera Qureshi, Muhammad Ibrar Abbas, Humaira Kalsoom, Fawad Nadeem, T. Chalapathi, L. Madhavi, R. Suresh, S. Palaniammal, Nivetha Martin, Florentin Smarandache, S. A. Edalatpanah, Rafif Alhabib, A. A. Salama, Memet Şahin, Abdullah Kargın, Murat Yücel, Dimacha Dwibrang Mwchahary, Bhimraj Basumatary, R. S. Alghamdi, N. O. Alshehri, Shigui Du, Rui Yong, Jun Ye, Vasantha Kandasamy, Ilanthenral Kandasamy, Muhammad Saeed, Muhammad Saqlain, Asad Mehmood, Khushbakht Naseer, Sonia Yaqoob, Sudipta Gayen, Sripati Jha, Manoranjan Kumar Singh, Ranjan Kumar, Huseyin Kamaci, Shawkat Alkhazaleh, Anas Al-Masarwah, Abd Ghafur Ahmad, Merve Sena Uz, Akbar Rezaei, Mohamed Grida, Rehab Mohamed, Abdelnaser H. Zaid.
Author: Xiaohong Zhang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 17
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Book Description
The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups.
Author: Wangtao Yuan
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
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Book Description
Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained.
Author: Vasantha Kandasamy
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
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Book Description
In this paper, authors define the NeutroAlgebra of neutrosophic triplets groups. We prove the existence theorem for NeutroAlgebra of neutrosophic triplet groups. Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained.
