Ansari Safoora Samreen Jamal Abdul Nasir - Department 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, ۴۲۳ ۱۰۱, M.S., India
Kishor Fakira Pawar - Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, ۴۲۵ ۰۰۱ M.S., India

In this paper c-system , n-system and complete prime Γ-radical in a Γ-semihypergroup are introduced and studied whiledefinition of m-system has been revised. Maximal Γ-hyperideals are studied and the conditions under which maximal Γ-hyperideals are prime and vice versa are investigated. It is proved that intersection of distinct maximal Γ-hyperideals in Γ-semihypergroup is non-empty. Relations between completely prime Γ-hyperideals, c-system and complete prime Γ-radicals are examined.

Systems, Γ-semihypergroup, Γ-hyperideal, Γ-radical