• PROPERTIES OF LATTICE ORDERED GROUPS AND ORDERED Γ- SEMIGROUPS

Abstract

In this paper, we present the properties of lattice ordered groups derived from the properties of partially ordered groups. The notion of Γ-semi groups was introduced by Sen in 1981. The concept of Γ- semigroups is a generalization of the concept of semigroups Many classical notions of semigroups have been extended to Γ -semigroups, ( S, Γ , ) is called an ordered Γ -semigroup if S is a Γ -semigroup and ( S, ) is a partially ordered set such that a≤b⇒a γ c≤b γ c and c γ a≤c γ b for all a,b,c ϵ S and γ ϵ Γ