On Green's relations, 2-regularity and quasi-ideals in Γ-semigroups.

In this paper, we introduce the definition of ( m, n)-regularity in Γ-semigroups. We investigate and characterize the 2-regular class of Γ-semigroups using Green's relations. Extending and generalizing the Croisot's Theory of Decomposition for Γ-semigroups, we introduce and study the absorbent and regular absorbent Γ-semigroups. We approach this problem by examining quasi-ideals using Green's relations. [ABSTRACT FROM AUTHOR]