On bi-ideals of Γ-semihyperrings
The concept of Γ-semihyperrings is a generalization of semirings, semihyperrings and Γ-semirings. The notion of bi-ideals and minimal bi-ideals in Γ-semihyperrings is introduced with several examples. We also made some ideal theoretic characterization of bi-ideals and minimal bi-ideals in Γ-semihyp...
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| Format: | Article |
| Language: | English |
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University of Mohaghegh Ardabili
2023-12-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_2562_0257444165c6a60e3029e8d6efcd2434.pdf |
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| author | Jitendrasing Jaysing Patil Kishor F. Pawar |
| author_facet | Jitendrasing Jaysing Patil Kishor F. Pawar |
| author_sort | Jitendrasing Jaysing Patil |
| collection | DOAJ |
| description | The concept of Γ-semihyperrings is a generalization of semirings, semihyperrings and Γ-semirings. The notion of bi-ideals and minimal bi-ideals in Γ-semihyperrings is introduced with several examples. We also made some ideal theoretic characterization of bi-ideals and minimal bi-ideals in Γ-semihyperrings. Then the notion of bi-simple Γ-semihyperrings is introduced and it is proved that ``If R is a Γ-semihyperring without zero, then R is a bi-simple Γ-semihyperring if and only if (k)b=R, for all k∈ R, where (k)b is a bi-ideal generated by k." |
| format | Article |
| id | doaj-art-333d6d1fb09b46d589fc67f1c91e76f3 |
| institution | Kabale University |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-333d6d1fb09b46d589fc67f1c91e76f32025-08-20T03:50:02ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662023-12-0111218319510.22098/jhs.2023.25622562On bi-ideals of Γ-semihyperringsJitendrasing Jaysing Patil0Kishor F. Pawar1Department of Mathematics, Indraraj Arts, Commerce and Science college, Sillod, Dr. Babashasheb Ambedkar Marathwada University Aurangabad- 431 112, India.Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., IndiaThe concept of Γ-semihyperrings is a generalization of semirings, semihyperrings and Γ-semirings. The notion of bi-ideals and minimal bi-ideals in Γ-semihyperrings is introduced with several examples. We also made some ideal theoretic characterization of bi-ideals and minimal bi-ideals in Γ-semihyperrings. Then the notion of bi-simple Γ-semihyperrings is introduced and it is proved that ``If R is a Γ-semihyperring without zero, then R is a bi-simple Γ-semihyperring if and only if (k)b=R, for all k∈ R, where (k)b is a bi-ideal generated by k."https://jhs.uma.ac.ir/article_2562_0257444165c6a60e3029e8d6efcd2434.pdfγ-semihyperringbi-idealsminimal bi-idealsbi-simple γ-semihyperring |
| spellingShingle | Jitendrasing Jaysing Patil Kishor F. Pawar On bi-ideals of Γ-semihyperrings Journal of Hyperstructures γ-semihyperring bi-ideals minimal bi-ideals bi-simple γ-semihyperring |
| title | On bi-ideals of Γ-semihyperrings |
| title_full | On bi-ideals of Γ-semihyperrings |
| title_fullStr | On bi-ideals of Γ-semihyperrings |
| title_full_unstemmed | On bi-ideals of Γ-semihyperrings |
| title_short | On bi-ideals of Γ-semihyperrings |
| title_sort | on bi ideals of γ semihyperrings |
| topic | γ-semihyperring bi-ideals minimal bi-ideals bi-simple γ-semihyperring |
| url | https://jhs.uma.ac.ir/article_2562_0257444165c6a60e3029e8d6efcd2434.pdf |
| work_keys_str_mv | AT jitendrasingjaysingpatil onbiidealsofgsemihyperrings AT kishorfpawar onbiidealsofgsemihyperrings |