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, Γ ) is a Γ-semigroup and ( S, ≤ ) is a partially ordered set such that a ≤ b ⇒ a r c ≤ b r c and c r a ≤ c r b for all a, b, c € s  and r € Γ
 

Index Terms—Partially ordered groups, Lattice ordered groups, semi groups, Γ semi groups and ordered Γ semi groups
V. B Subrahmanyeswara Rao Seetamraju is working as Assistant Professor of mathematics and Controller of Examinations at VKR, VNB & AGK College of Engineering, Gudivada.
A. Anjaneyulu is with the department of Mathematics, VSR & NVR College, Tenali, A. P.
Sridevi. S is working as Assistant Professor of mathematics at VKR, VNB & AGK College of Engineering, Gudivada.

Cite: V. B. Subrahmanyeswara Rao Seetamraju, Anjaneyulu A., and Sridevi S., "Properties of Lattice Ordered Groups and Γ - Semi Groups," International Journal of Applied Physics and Mathematics  vol. 2, no. 4, pp. 290-292, 2012.