Characterizations of gamma-AG^{**}-groupoids by the properties their gamma-ideals

In this paper we have discusses {\Gamma}-left, {\Gamma}-right, {\Gamma}-bi-, {\Gamma}-quasi-, {\Gamma}-interior and {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and regular {\Gamma}-AG^{**}-groupoids. Moreover we have proved that the set of {\Gamma}-ideals in a regular {\Gamma}-AG^{**}-groupoid form a semilattice structure. Also we have characterized a regular {\Gamma}-AG^{**}-groupoid in terms of left ideals.