Jitendrasing Jaysing Patil - Department of Mathematics, Indraraj Arts, Commerce and Science college, Sillod, Dr. Babashasheb Ambedkar Marathwada University Aurangabad- ۴۳۱ ۱۱۲, India.
Kishor Fakira Pawar - Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, ۴۲۵ ۰۰۱ M.S., India

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.

Quasi-ideal, Minimal quasi-ideal, Quasi-simple, Γ-semihyperring