on certain γ-hyperideals in γ-semihypergroups

In this paper pseudo symmetric gamma;-hyperideal in gamma;semihypergroups is introduced and characterized. it is proved thatthe class of pseudo symmetric gamma;-semihypergroups contains left (right) duo gamma;-semihypergroups, quasi commutative gamma;-semihypergroups with unity, left (right) pseudo commutative gamma;-semihypergroups and idempotent gamma;-semihypergroups. the notions of completely prime gamma;hyperideal, semiprime gamma;-hyperideal, partially semiprime gamma;- hyperideal are also defined and completely prime gamma;-hyperideal of a gamma;semihypergroup has been characterized in terms of prime gamma;- hyperideal and pseudo symmetric gamma;-hyperideal. the characterization of completely semiprime gamma;-hyperideals of gamma;-semihypergroupsis presented. in gamma;-semihypergroup n-semiprime gamma;-hyperideal and npartially semiprime gamma;-hyperideal are introduced as a generalization of semiprime gamma;-hyperideal and partially semiprime gamma;-hyperideal of gamma;-semihypergroup respectively. the notion of semi-extension of gamma;hyperideal in gamma;-semihypergroup has also been defined. some related results are proved along with establishing the relationship between n-semiprime gamma;-hyperideals and semi-extension of gamma;-hyperideal in commutative gamma;-semihypergroups.