On bi-ideals of Γ-semihyperrings

The concept of Γ-semihyperrings is a generalization of semirings, semihyperrings and  Γ-semirings. The notion of bi-ideals and minimal bi-ideals in Γ-semihyperrings is introduced with several examples. We also made some ideal theoretic characterization of bi-ideals and minimal bi-ideals in Γ-semihyperrings. Then the notion of bi-simple Γ-semihyperrings is introduced and it is proved that ``If R is a Γ-semihyperring without zero, then R is a bi-simple Γ-semihyperring if and only if (k)b=R, for all k∈ R, where (k)b is a bi-ideal generated by k."

Keywords:

Γ-semihyperring , Bi-ideals , Minimal bi-ideals , bi-simple Γ-semihyperring