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, equiprime 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.