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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2024-0079 |
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| Summary: | 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. |
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| ISSN: | 2391-5455 |