A study on weak hyperfilters of ordered semihypergroups
In this paper, the notion of weak hyperfilters of an ordered semihypergroup is introduced, and several related properties and applications are given. In particular, we discuss the relationship between the weak hyperfilters and the prime hyperideals in ordered semihypergroups. Furthermore, we define...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021256?viewType=HTML |
| _version_ | 1818877371583823872 |
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| author | Jian Tang Xiang-Yun Xie Ze Gu |
| author_facet | Jian Tang Xiang-Yun Xie Ze Gu |
| author_sort | Jian Tang |
| collection | DOAJ |
| description | In this paper, the notion of weak hyperfilters of an ordered semihypergroup is introduced, and several related properties and applications are given. In particular, we discuss the relationship between the weak hyperfilters and the prime hyperideals in ordered semihypergroups.
Furthermore, we define and investigate the equivalence relation ${\mathcal W}$ on an ordered semihypergroup by weak hyperfilters.
We establish the relation of the equivalence relation ${\mathcal W}$ and Green's relations of an ordered semihypergroup.
Finally, characterizations of intra-regular (duo) ordered semihypergroups are given by the properties of weak hyperfilters. |
| first_indexed | 2024-12-19T13:57:13Z |
| format | Article |
| id | doaj.art-3437525ce2514149afab253bd91c6b23 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T13:57:13Z |
| publishDate | 2021-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3437525ce2514149afab253bd91c6b232022-12-21T20:18:34ZengAIMS PressAIMS Mathematics2473-69882021-02-01654319433010.3934/math.2021256A study on weak hyperfilters of ordered semihypergroupsJian Tang0Xiang-Yun Xie1Ze Gu21. School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P. R. China2. School of Mathematics and Computational Science, Wuyi University, Guangdong, P. R. China3. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P. R. ChinaIn this paper, the notion of weak hyperfilters of an ordered semihypergroup is introduced, and several related properties and applications are given. In particular, we discuss the relationship between the weak hyperfilters and the prime hyperideals in ordered semihypergroups. Furthermore, we define and investigate the equivalence relation ${\mathcal W}$ on an ordered semihypergroup by weak hyperfilters. We establish the relation of the equivalence relation ${\mathcal W}$ and Green's relations of an ordered semihypergroup. Finally, characterizations of intra-regular (duo) ordered semihypergroups are given by the properties of weak hyperfilters.http://www.aimspress.com/article/doi/10.3934/math.2021256?viewType=HTMLordered semihypergroupweak hyperfiltergreen's relationintra-regular (duo) ordered semihypergroup |
| spellingShingle | Jian Tang Xiang-Yun Xie Ze Gu A study on weak hyperfilters of ordered semihypergroups AIMS Mathematics ordered semihypergroup weak hyperfilter green's relation intra-regular (duo) ordered semihypergroup |
| title | A study on weak hyperfilters of ordered semihypergroups |
| title_full | A study on weak hyperfilters of ordered semihypergroups |
| title_fullStr | A study on weak hyperfilters of ordered semihypergroups |
| title_full_unstemmed | A study on weak hyperfilters of ordered semihypergroups |
| title_short | A study on weak hyperfilters of ordered semihypergroups |
| title_sort | study on weak hyperfilters of ordered semihypergroups |
| topic | ordered semihypergroup weak hyperfilter green's relation intra-regular (duo) ordered semihypergroup |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021256?viewType=HTML |
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