Ideals on neutrosophic extended triplet groups
In this paper, we introduce the concept of (prime) ideals on neutrosophic extended triplet groups (NETGs) and investigate some related properties of them. Firstly, we give characterizations of ideals generated by some subsets, which lead to a construction of a NETG by endowing the set consisting of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022264?viewType=HTML |
| _version_ | 1818976340777369600 |
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| author | Xin Zhou Xiao Long Xin |
| author_facet | Xin Zhou Xiao Long Xin |
| author_sort | Xin Zhou |
| collection | DOAJ |
| description | In this paper, we introduce the concept of (prime) ideals on neutrosophic extended triplet groups (NETGs) and investigate some related properties of them. Firstly, we give characterizations of ideals generated by some subsets, which lead to a construction of a NETG by endowing the set consisting of all ideals with a special multiplication. In addition, we show that the set consisting of all ideals is a distributive lattice. Finally, by introducing the topological structure on the set of all prime ideals on NETGs, we obtain the necessary and sufficient conditions for the prime ideal space to become a T1-space and a Hausdorff space. |
| first_indexed | 2024-12-20T16:10:18Z |
| format | Article |
| id | doaj.art-816a973062c1455b85f303b5e8dc8598 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T16:10:18Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-816a973062c1455b85f303b5e8dc85982022-12-21T19:34:01ZengAIMS PressAIMS Mathematics2473-69882022-01-01734767477710.3934/math.2022264Ideals on neutrosophic extended triplet groupsXin Zhou0Xiao Long Xin11. School of Science, Xi'an Polytechnic University, 710048 Xi'an, China1. School of Science, Xi'an Polytechnic University, 710048 Xi'an, China 2. School of Mathematics, Northwest University, Xi'an, 710127, ChinaIn this paper, we introduce the concept of (prime) ideals on neutrosophic extended triplet groups (NETGs) and investigate some related properties of them. Firstly, we give characterizations of ideals generated by some subsets, which lead to a construction of a NETG by endowing the set consisting of all ideals with a special multiplication. In addition, we show that the set consisting of all ideals is a distributive lattice. Finally, by introducing the topological structure on the set of all prime ideals on NETGs, we obtain the necessary and sufficient conditions for the prime ideal space to become a T1-space and a Hausdorff space.https://www.aimspress.com/article/doi/10.3934/math.2022264?viewType=HTMLnetgidealprime ideal space |
| spellingShingle | Xin Zhou Xiao Long Xin Ideals on neutrosophic extended triplet groups AIMS Mathematics netg ideal prime ideal space |
| title | Ideals on neutrosophic extended triplet groups |
| title_full | Ideals on neutrosophic extended triplet groups |
| title_fullStr | Ideals on neutrosophic extended triplet groups |
| title_full_unstemmed | Ideals on neutrosophic extended triplet groups |
| title_short | Ideals on neutrosophic extended triplet groups |
| title_sort | ideals on neutrosophic extended triplet groups |
| topic | netg ideal prime ideal space |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022264?viewType=HTML |
| work_keys_str_mv | AT xinzhou idealsonneutrosophicextendedtripletgroups AT xiaolongxin idealsonneutrosophicextendedtripletgroups |