Ideal theory in  -semihyperrings

Document Type : Regular Paper


Department of Mathematics, Yazd University, Yazd, Iran


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

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