Semilattice strongly regular relations on ordered n-ary semihypergroups
In this paper, we introduce the concept of j-hyperfilters, for all positive integers 1≤j≤n and n≥2, on (ordered) n-ary semihypergroups and establish the relationships between j-hyperfilters and completely prime j-hyperideals of (ordered) n-ary semihypergroups. Moreover, we investigate the properties...
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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.2022031?viewType=HTML |
| _version_ | 1818939540810760192 |
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| author | Jukkrit Daengsaen Sorasak Leeratanavalee |
| author_facet | Jukkrit Daengsaen Sorasak Leeratanavalee |
| author_sort | Jukkrit Daengsaen |
| collection | DOAJ |
| description | In this paper, we introduce the concept of j-hyperfilters, for all positive integers 1≤j≤n and n≥2, on (ordered) n-ary semihypergroups and establish the relationships between j-hyperfilters and completely prime j-hyperideals of (ordered) n-ary semihypergroups. Moreover, we investigate the properties of the relation N, which is generated by the same principal hyperfilters, on (ordered) n-ary semihypergroups. As we have known from [21] that the relation N is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on n-ary semihypergroups where n≥3. However, we provide a sufficient condition that makes the previous conclusion true on n-ary semihypergroups and ordered n-ary semihypergroups where n≥3. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their N-classes. As an application of the results, a related problem posed by Tang and Davvaz in [31] is solved. |
| first_indexed | 2024-12-20T06:25:23Z |
| format | Article |
| id | doaj.art-ea69c9e0c1d546e1b388e6b826904fe7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T06:25:23Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ea69c9e0c1d546e1b388e6b826904fe72022-12-21T19:50:18ZengAIMS PressAIMS Mathematics2473-69882022-01-017147849810.3934/math.2022031Semilattice strongly regular relations on ordered n-ary semihypergroupsJukkrit Daengsaen0Sorasak Leeratanavalee11. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand2. Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandIn this paper, we introduce the concept of j-hyperfilters, for all positive integers 1≤j≤n and n≥2, on (ordered) n-ary semihypergroups and establish the relationships between j-hyperfilters and completely prime j-hyperideals of (ordered) n-ary semihypergroups. Moreover, we investigate the properties of the relation N, which is generated by the same principal hyperfilters, on (ordered) n-ary semihypergroups. As we have known from [21] that the relation N is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on n-ary semihypergroups where n≥3. However, we provide a sufficient condition that makes the previous conclusion true on n-ary semihypergroups and ordered n-ary semihypergroups where n≥3. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their N-classes. As an application of the results, a related problem posed by Tang and Davvaz in [31] is solved.https://www.aimspress.com/article/doi/10.3934/math.2022031?viewType=HTMLordered semihypergroupn-ary semihypergrouphyperidealhyperfilter |
| spellingShingle | Jukkrit Daengsaen Sorasak Leeratanavalee Semilattice strongly regular relations on ordered n-ary semihypergroups AIMS Mathematics ordered semihypergroup n-ary semihypergroup hyperideal hyperfilter |
| title | Semilattice strongly regular relations on ordered n-ary semihypergroups |
| title_full | Semilattice strongly regular relations on ordered n-ary semihypergroups |
| title_fullStr | Semilattice strongly regular relations on ordered n-ary semihypergroups |
| title_full_unstemmed | Semilattice strongly regular relations on ordered n-ary semihypergroups |
| title_short | Semilattice strongly regular relations on ordered n-ary semihypergroups |
| title_sort | semilattice strongly regular relations on ordered n ary semihypergroups |
| topic | ordered semihypergroup n-ary semihypergroup hyperideal hyperfilter |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022031?viewType=HTML |
| work_keys_str_mv | AT jukkritdaengsaen semilatticestronglyregularrelationsonorderednarysemihypergroups AT sorasakleeratanavalee semilatticestronglyregularrelationsonorderednarysemihypergroups |