Decomposition of commutative ordered Γ-semigroups into archimedean components

The greatest subgroup of a semigroup in Γ-semigroups

“…In this paper, we follow the definition as in 1986 which we shall state in a sequel. Some examples of Γ-semigroups can be seen in [4,4,9]. Many classical notions of semigroups have been extended to Γ-semigroups by some authors [1,2,3,4,7,8,9,10].…”

“…then we also write AΓB as aΓB, and similarly if B = {b} [9]. In [1], the Green's relations L, R and H on a Γ-semigroup S are defined by the following rules:…”