  The concept of hypergroup is generalization of group, first was introduced by
Marty [9]. This theory had applications to several domains. Marty had applied
them to groups, algebraic functions and rational functions. M. Krasner has
studied the notion of hyperring in [11]. G.G Massouros and C.G Massouros
defined hyperringoids and apply them in generalization of rings in [10]. They
also defined fortified hypergroups as a generalization of divisibility in
algebraic structures and use them in Automata and Language theory. T.
Vougiouklis has defined the representations and fundamental relations in
hyperrings in [14, 15]. R. Ameri, H. Hedayati defined k-hyperideals in
semihyperrings in [2]. B. Davvaz has defined some relations in hyperrings and
prove Isomorphism theorems in [7]. The aim of this article is to initiate the
study of semihyperrings and characterize it with hyperideals. In this article
we defined semihyperrings, hyperideals, prime, semiprime, irreducible, strongly
irreducible hyperideals, m-systems, p-systems, i-systems and regular
semihyperrings. We also shown that the lattice of irreducible hyperideals of
semihyperring R admits the structure of topology, which is called irreducible
spectrum topology.

Group Theory