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On quasi-ideals of Γ-semihyperrings | ||
| Journal of Hyperstructures | ||
| دوره 8، شماره 2، اسفند 2019، صفحه 123-134 اصل مقاله (97.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2019.2619 | ||
| نویسندگان | ||
| Jitendrasing Jaysing Patil* 1؛ Kishor Fakira 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 quasi-ideals, minimal quasi-ideals for Γsemihyperrings are introduced. Characterization of quasi-ideals and of minimal quasi-ideals of Γ-semihyperring with the help of ideals of Γ-semihyperrings have been taken into account. It is proved that for a Γ-semihyperring R with zero, one can find a quasi-ideal of R generated by X, where X is any non empty subset of R. Also the notion of quasi-simple Γ-semihyperring is introduced and proved some properties in this respect. | ||
| کلیدواژه‌ها | ||
| Quasi-ideal؛ Minimal quasi-ideal؛ Quasi-simple؛ Γ-semihyperring | ||
| مراجع | ||
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[1] F. Marty, Sur une generalization de la notion de groupe, 8-eme Congress Math.Scandinaves, Stockholm, (1934), 45-49. [2] K. Iseki, Quasi-ideals in Semirings without Zero, Proc. Japan Acad., 34 (1958),79-84. [3] K. Pawar, J. Patil and B. Davvaz, On a regular Γ- semihyperring and idempotent Γ- semihyperring, Kyungpook Math. J.,59 (2019), 35-45. [4] O. Steinfeld,On ideals quotients and prime ideals, Acta. Math. Acad. Sci. Uuge.4 (1953), 289-298. [5] O. Steinfeld,Uber die Quasiideale von Halbgruppen,Publ. Math. Debrecen, 4 (1956), 262-275. [6] R. Chinram,On Quasi-Gamma-ideals in Γ-Semigroups, Science Asia, 32 (2006),351-353. [7] R. Jagatap and Y. Pawar, Quasi ideals and minimal quasi ideals in Γ- semirings,Novi Sad J.Math.Serbia, 39(2) (2009),79-87. [8] S. Ostadhadi-Dehkordi and B. Davvaz, Ideal theory in Γ- semihyperrings, Iran. J. Sci. Technol. A. , 37(3) (2013), 251-263. | ||
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