Abstract
Let G be a group with identity e, R be a G-graded ring with unity 1 and M be a G-graded R-module. In this article, we introduce the concept of graded quasi multiplication modules, where graded M is said to be graded quasi multiplication if for every graded weakly prime R-submodule N of M, N = IM for some graded ideal I of R. Also, we introduce the concept of graded absorbing multiplication modules; M is said to be graded absorbing multiplication if M has no graded 2-absorbing R-submodules or for every graded 2-absorbing R-submodule N of M, N = IM for some graded ideal I of R. We prove many results concerning graded weakly prime submodules and graded 2-absorbing submodules that will be useful in providing several properties of the two classes of graded quasi multiplication modules and graded absorbing multiplication modules.