On some properties of normal ?-ideals in normal ?-semigroups

Abstract

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