On systems, maximal Γ-hyperideals and complete prime Γ-radicals in Γ-semihypergroups

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.

Keywords:

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