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

Abstract

We introduce the concept of normal T-ideal and bi-T-ideal in normal T- semigroups. We characterize the normal T-semigroup and normal regular T-semigroup in terms of elementary properties of bi-T-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1; I2 are any two normal T- ideals of a T-semigroup S, then their product I1TI2 and I2TI1 are also normal T-ideals of S and I1TI2 = I2TI1. Finally, we show that the minimal normal T-ideal of a T-semigroup S is a T-group.