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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 wehave proved that the set of {\Gamma}-ideals in a regular{\Gamma}-AG^{**}-groupoid form a semilattice structure. Also we havecharacterized a regular {\Gamma}-AG^{**}-groupoid in terms of left ideals.

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