Characterizations of intra-regular gamma AG-groupoids by the properties of their gamma ideals

We have characterized an intra-regular {\Gamma}-AG^{}-groupoids by using the properties of {\Gamma}-ideals (left, right, two-sided ), {\Gamma}-interior, {\Gamma}-quasi, {\Gamma}-bi and {\Gamma}-generalized bi and {\Gamma}-(1,2)). We have prove that all the {\Gamma}-ideals coincides in an intra-regular {\Gamma}-AG^{}-groupoids. It has been examined that all the {\Gamma}-ideals of an intra-regular {\Gamma}-AG^{}-groupoids are {\Gamma}-idempotent. In this paper we define all {\Gamma}-ideals in {\Gamma}-AG^{}-groupoids and we generalize some results.