Graded 2-Absorbing Submodules over Non-Commutative Rings

Abstract

Let R be a non-commutative G-graded ring with unity and M be a G-graded left R-module. We define the concept of a graded 2-absorbing submodule and show that if the ring is commutative, then the concept is the same as the original definition of that of K. Al-Zoubi and R. Abu-Dawwas. We give an example to show that in general these two concepts are different. Many properties of graded 2-absorbing submodules are introduced which are similar to the results for commutative rings.