ON SOME PROPERTIES OF NORMAL Γ-IDEALS IN NORMAL Γ-SEMIGROUPS

We introduce the concept of normal Gamma-ideal and bi-Gamma-ideal in normal Gamma-semigroups semigroups. We characterize the (normal) Gamma-semigroup and normal regular Gamma-semigroup in terms of elementary properties of bi-Gamma-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I-1, I-2 are any two normal Gamma-ideals of a Gamma-semigroup S, then their product I-1 Gamma I-2 and I-2 Gamma I-1 are also normal Gamma-ideals of S and I-1 Gamma I-2 = I-2 Gamma I-1. Finally, we show that the minimal normal Gamma-ideal of a Gamma-semigroup S is a Gamma-group.