A Note on Minimal Bi-Ideals in Ordered Γ-Semigroups
Ronnason Chinram, Kittisak Tinpun · 2008
The notion of Γ-semigroups was introduced by Sen in 1981. The concept of Γ-semigroups is a generalization of the concept of semi-groups. Many classical notions of semigroups have been extended to Γ-semigroups. (S,Γ,≤) is called an ordered Γ-semigroup if (S,Γ) is a Γ-semigroup and (S,≤) is a partially ordered set such that a ≤ b ⇒ aγc ≤ bγc and cγa ≤ cγb for all a, b, c ∈ S and γ ∈ Γ. A subΓ-semigroup B of an ordered Γ-semigroup S is called a bi-ideal of S if BΓSΓB ⊆ B and (B] ⊆ B. In this note, we study some properties of bi-ideals and minimal bi-ideals of ordered Γ-semigroups.