On Prime and semiprime ideals of \Gamma-semihyperrings

The \Gamma-semihyperring is  a generalization of the concepts of a semiring, a semihyperring and a \Gamma-semiring. In this paper, the notions of completely prime ideals and prime radicals for \Gamma-semihyperring are introduced and studied some important properties accordingly. We also introduced the notions of m-system and complete m-system. Then characterizations of prime ideals and completely prime ideals of \Gamma-semihyperring with the help of m-system and complete m-system has been taken into account. It is our attempt to find a bridge between semiprime (completely semiprime) ideals and prime (completely prime) ideals of a \Gamma-semihyperring.

Keywords:

m-system , complete m-system , additively idempotent Gamma-semihyperring