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On certain Γ-hyperideals in Γ-semihypergroups | ||
| Journal of Hyperstructures | ||
| دوره 9، شماره 2، اسفند 2020، صفحه 34-51 اصل مقاله (288.24 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2020.2630 | ||
| نویسندگان | ||
| Ansari Safoora Samreen Jamal Abdul Nasir* 1؛ Kishor Fakira Pawar2 | ||
| 1Department of Mathematics, S.N.J.B.’s K.K.H.A. Arts, S.M.G.L. Commerce & S.P.H.J. Science College, Chandwad, District 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 | ||
| In this paper pseudo symmetric Γ-hyperideal in Γsemihypergroups is introduced and characterized. It is proved that the class of pseudo symmetric Γ-semihypergroups contains left (right) duo Γ-semihypergroups, quasi commutative Γ-semihypergroups with unity, left (right) pseudo commutative Γ-semihypergroups and idempotent Γ-semihypergroups. The notions of completely prime Γhyperideal, semiprime Γ-hyperideal, partially semiprime Γ- hyperideal are also defined and completely prime Γ-hyperideal of a Γsemihypergroup has been characterized in terms of prime Γ- hyperideal and pseudo symmetric Γ-hyperideal. The characterization of completely semiprime Γ-hyperideals of Γ-semihypergroups is presented. In Γ-semihypergroup n-semiprime Γ-hyperideal and npartially semiprime Γ-hyperideal are introduced as a generalization of semiprime Γ-hyperideal and partially semiprime Γ-hyperideal of Γ-semihypergroup respectively. The notion of semi-extension of Γhyperideal in Γ-semihypergroup has also been defined. Some related results are proved along with establishing the relationship between n-semiprime Γ-hyperideals and semi-extension of Γ-hyperideal in commutative Γ-semihypergroups. | ||
| کلیدواژه‌ها | ||
| Γ-semihypergroup؛ Γ-hyperideal؛ Pseudo Symmetric Γ-hyperideal؛ Completely Prime Γ-hyperideal؛ n-semiprime Γ-htperideal | ||
| مراجع | ||
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