Let R be a noncommutative ring with identity. We define the notion of a 2-absorbing ideal and show that if the ring is commutative, then the notion is the same as the original definition that of Badawi. We give an example to show that in general these two notions are different. Many properties of 2-absorbing ideals are proved which are similar to the results for commutative rings.

2-absorbing ideal, strong 2-absorbing ideal, prime ideal, completely prime ideal.