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Bi-interior, quasi-interior and bi-quasi-interior Γ-hyperideal in Γ-semihyperring | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 1، 2023، صفحه 1-17 اصل مقاله (302.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2509 | ||
| نویسندگان | ||
| Chaitanya B. Kumbharde1؛ Kishor F. Pawar2؛ Safoora J. Ansari* 1 | ||
| 1Department of Mathematics, SNJB's KKHA Arts, SMGL Commerce & SPHJ Science College, Chandwad, Dist. Nashik, 423 101, M.S. India | ||
| 2Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., India | ||
| چکیده | ||
| The concept of a Γ-semihyperring is a generalization of a semiring, semihyperring, Γ-semiring. In this Paper we introduce the notion of bi-interior Γ-hyperideals, quasi-interior Γ-hyperideals and bi-quasi-interior Γ-hyperideals in a Γ-semihyperring as a generalization of Γ-hyperideal, left-Γ-hyperideal, right-Γ- hyperideals, bi Γ-hyperideal, quasi Γ-hyperideal, interior Γ-hyperideals of Γ-semihyperring. We studied the properties of these Γ-hyperideals and characterized them in simple Γ-semihyperring and regular Γ-semihyperring | ||
| کلیدواژه‌ها | ||
| Γ-semihyperring؛ bi-interior Γ- hyperideals؛ quasi-interior Γ- hyperideals؛ bi-quasi-interior Γ- hyperideals | ||
| مراجع | ||
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[1] S. J. Ansari and K.F.Pawar,On Certain Γ-Hyperideals in Γ-Semihypergroups,Journal of Hyperstructures, 9(2)(2020),34-51. [2] S. M. Anvariyeh, S. Mirvakili, and B. Davvaz, On Γ-Hyperideals in Γ-Semihypergroups, Carpathian Journal of Mathematics, (2010), 11-23. [3] R. A. Good and D. R. Hughes, Associated Groups for a Semigroup, Bulletin of the American Mathematical Society, 58 (1952), 624-625. [4] K. Iseki, Quasi-ideals in Semirings without Zero, Proc. Japan Acad., 34 (1958),79-84. [5] R. Jagtap and Y. Pawar Quasi Ideals and Minimal Quasi Ideals in Γ-Semiring,Novi. SAD. Jour. of Mathematics(serebia), 39(2) (2009), 79-87. [6] S. Lajos and A. Szsz, On the Bi-Ideals in Associative Rings, Proceeding of the Japan Academy, 46(6) (1970), 505-507. [7] F. Marty, Sur une g´en´eralization de la notion de groupe , In proceedings of 8th Congress Math. Scandinaves, Stockholm, Sweden (1934), 45-49. [8] S. Ostadhadi-Dehkordi and B. Davvaz, Ideal Theory in Γ-Semihyperrings,Iran.J. Sci. Technol. A., 37(3) (2013), 251-263. [9] J. J. Patil, On Bi-Ideals of Γ-Semihyperrings, Journal of Hyperstructures, 11(2)(2023). [10] J. J. Patil, On Quasi-Ideals of Γ-semihyperrings, Journal of Hyperstructures,8(2), (2020). [11] K. F. Pawar and S. J. Ansari, On System, Maximal Γ-Hyperideals and Complete prime Γ-radicals in Γ-Semihypergroups, Journal of Hyperstructures, 8(2) (2019),135-149. [12] K. Pawar, J. Patil and B. Davvaz, On a Regular Γ- Semihyperring and Idempo-tent Γ- Semihyperring, Kyungpook Math. J., 59 (2019), 35-45. [13] M.K.Rao,Quasi-Interior Ideals and Fuzzy Quasi-Interior Ideals of Γ-Semirings,Ann. Fuzzy Math. Inform,18(1)(2019),31-43. [14] M. K. Rao, A study of Bi-Quasi-Interior Ideal as a New Generalization of Ideal of Generalization of Semiring, Bull. Int. Math. Virtual Inst, 8(3), (2018), 519-535. [15] M. K. Rao, Bi-Interior Ideals of Semigroups, Discuss. Math. Gen. Algebra Appl.,38 (2018), 69 - 78. [16] M.Shabir,A.Ali and S. Batool,A Note on Qusai-Ideals in Semirings,SoutheastAsian Bulletin of Mathematics,27(5),923-928. | ||
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