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

A. Basar, M. Y. Abbasi

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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.

Keywords

T-semigroup, normal ideal