Prime Strong Ideals of S-semigroup

A seminearring is a generalization of the notion nearring in which the elements need not have an additive inverse. A S-semigroup is a generalization of the notion N-group in which the scalars are from seminearring. In this paper, we define various prime strong ideals of a S-semigroup and obtain the relationship among them. We also establish the connections between completely equiprime, equi-prime and completely prime strong ideals of a S-semigroup. The obtained results are illustrated with the suitable examples. We also prove that every equiprime strong ideal of a S-semigroup is 3-prime strong ideal. In addition, we show that (P: Q)_S is strong ideal of a seminearring S and prove related results.