On prime spaces of neutrosophic extended triplet groups
This article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) NN, denoted by Prim(N){\rm{Prim}}\left(N). First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topologica...
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De Gruyter
2024-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0079 |
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| _version_ | 1850067063225188352 |
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| author | Zhou Xin Xin Xiao Long |
| author_facet | Zhou Xin Xin Xiao Long |
| author_sort | Zhou Xin |
| collection | DOAJ |
| description | This article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) NN, denoted by Prim(N){\rm{Prim}}\left(N). First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topological space XX is an SSSS-space if and only if XX is homeomorphic to the space Prim(N){\rm{Prim}}\left(N) of some weak commutative NETG. In addition, we prove that there exists an adjunction between the dual category of weak commutative NETGs and the category of SSSS-spaces. Finally, we further study the categorical relation between idempotent weak commutative NETGs and that of SSSS-spaces, which leads to a conclusion that the category of idempotent weak commutative NETGs is equivalent to that of commutative idempotent semigroups. |
| format | Article |
| id | doaj-art-86bcff434597446fb465908944bf016c |
| institution | DOAJ |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-86bcff434597446fb465908944bf016c2025-08-20T02:48:30ZengDe GruyterOpen Mathematics2391-54552024-12-01221436010.1515/math-2024-0079On prime spaces of neutrosophic extended triplet groupsZhou Xin0Xin Xiao Long1School of Science, Xi’an Polytechnic University, 710048Xi’an, P. R. ChinaSchool of Science, Xi’an Polytechnic University, 710048Xi’an, P. R. ChinaThis article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) NN, denoted by Prim(N){\rm{Prim}}\left(N). First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topological space XX is an SSSS-space if and only if XX is homeomorphic to the space Prim(N){\rm{Prim}}\left(N) of some weak commutative NETG. In addition, we prove that there exists an adjunction between the dual category of weak commutative NETGs and the category of SSSS-spaces. Finally, we further study the categorical relation between idempotent weak commutative NETGs and that of SSSS-spaces, which leads to a conclusion that the category of idempotent weak commutative NETGs is equivalent to that of commutative idempotent semigroups.https://doi.org/10.1515/math-2024-0079weak commutative netgzariski topologytopological representationequivalence of categories20a1518b3054f65 |
| spellingShingle | Zhou Xin Xin Xiao Long On prime spaces of neutrosophic extended triplet groups Open Mathematics weak commutative netg zariski topology topological representation equivalence of categories 20a15 18b30 54f65 |
| title | On prime spaces of neutrosophic extended triplet groups |
| title_full | On prime spaces of neutrosophic extended triplet groups |
| title_fullStr | On prime spaces of neutrosophic extended triplet groups |
| title_full_unstemmed | On prime spaces of neutrosophic extended triplet groups |
| title_short | On prime spaces of neutrosophic extended triplet groups |
| title_sort | on prime spaces of neutrosophic extended triplet groups |
| topic | weak commutative netg zariski topology topological representation equivalence of categories 20a15 18b30 54f65 |
| url | https://doi.org/10.1515/math-2024-0079 |
| work_keys_str_mv | AT zhouxin onprimespacesofneutrosophicextendedtripletgroups AT xinxiaolong onprimespacesofneutrosophicextendedtripletgroups |