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

We introduce the concept of normal Γ-ideal and bi-Γ-ideal in normal Γsemigroups. We characterize the (normal) Γ-semigroup and normal regular Γ-semigroup in terms of elementary properties of bi-Γ-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1, I2 are any two normal Γideals of a Γ-semigroup S, then their product I1ΓI2 and I2ΓI1 are also normal Γ-ideals of S and I1ΓI2 = I2ΓI1. Finally, we show that the minimal normal Γ-ideal of a Γ-semigroup S is a Γ-group.