Ideal theory in  -semihyperrings

Abstract

The concept of  -semihyperring is a generalization of semiring, a generalization of semihyperring and a generalization of

 -semiring. Since the theory of ideals plays an important role in the theory of  - semihyperring, in this paper, we will make an intensive study of the notions of Noetherian, Artinian, simple and

regular

 -semihyperrings. The bulk of this paper is devoted to stating and proving analogues to several theorems in the theory of

 -semihyperrings.