Abstract

The algebraic system Γ-near rings was introduced by Satyanarayana. Tamizh and Ganesan introduced the concept of bi-ideals in near-rings [On bi-ideals of near-rings, Indian J. Pure Appl. Math., 18(11), 1002-1005(1987)]. Tamizh and Meenakumari defined the concept of bi-ideals in Γ-near-rings and characterized Γ-near-fields [Bi-Ideals of Gamma Near-Rings, Southeast Asian Bulletin of Mathematics(2004), 27: 983-988]. Satyanarayana, Yahya, Basar and Kuncham studied abstract affine Γ-nearrings [Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43-49]. Recently, Basar, Satyanarayana, Kuncham, Kumar and Yahya studied some relative ideals in Γ-nearrings [A note on relative Γ-ideals in abstract affine Γ-nearrings, GIS Science Journal, 8(10)(2021), 9-13]. In this paper, we study relative quasi-Γ-ideals and relative bi-Γ-ideals in Γ-near rings. We also proved nice characterizations of Γ-near rings by these basic relative Γ-ideals.