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On bi-ideals of Γ-semihyperrings | ||
| Journal of Hyperstructures | ||
| دوره 11، شماره 2، اسفند 2022، صفحه 183-195 اصل مقاله (292.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2562 | ||
| نویسندگان | ||
| Jitendrasing Jaysing Patil* 1؛ Kishor F. Pawar2 | ||
| 1Department of Mathematics, Indraraj Arts, Commerce and Science college, Sillod, Dr. Babashasheb Ambedkar Marathwada University Aurangabad- 431 112, India. | ||
| 2Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., India | ||
| چکیده | ||
| 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." | ||
| کلیدواژه‌ها | ||
| Γ-semihyperring؛ Bi-ideals؛ Minimal bi-ideals؛ bi-simple Γ-semihyperring | ||
| مراجع | ||
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[1] Iampan Aiyared, On Bi-ideals in Γ-semigroups, Lobachevskii Journal of Mathe-matics, 29(2) (2009), 68-72. [2] Iampan Aiyared, Note on Bi-ideals in Γ-semigroups, International Journal of Algebra, 3(4) (2009), 181-188. [3] R. Jagatap and Y. Pawar, Bi-ideals in Γ-semirings, Bulletin of the society of mathematicians banja luka, 6 (2016), 169-179. [4] J. Kaushik and M. Khan, On Bi-ideal in Γ-Semirings, Int. J. Contemp. Math.Sciences, 3 (2008), 1255-1260. [5] S. Lajos and F. Szasz, On the Bi-ideals in associative rings, Proc. Japan Acad.,49(6) (1970), 317-321. [6] S. Lajos and F. Szasz, On the Bi-ideals in Semigroups, Proc. Japan Acad., 46(1970), 505-507. [7] S. Lajos and F. Szasz, On the Bi-ideals in Semigroups II, Proc. Japan Acad., 47(1971), 837-839. [8] F Marty, Sur une generalization de la notion de groupe, 8th congres Math. Scandinaves, Stockholm, (9134), 45-49. [9] S. Ostadhadi-Dehkordi and B. Davvaz, Ideal theory in Γ- semihyperrings, Iranian Journal of Science and Technology A, 37(3) (2013), 251-263. [10] K. Pawar, J. Patil and B. Davvaz, On a regular Γ- semihyperring and idempotent Γ- semihyperring, Kyungpook Math. J., 59 (2019), 35-45. [11] J. Patil and K. Pawar, On Quasi ideals of Γ-semihyperrings, Journal of Hyper-stuctures, 8 (2) (2019), 123-134. [12] M. Shabir, A. Ali and S. Batool, A Note on Quasi-ideals in Semirings, Southeast Asian Bull. Of Math., 27 (2004), 923-928. | ||
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