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Let G be a group and g ∈ G. Let R be a commutative G-graded ring and M be a graded R-module. In this paper, we study some cases when R is strongly graded ring and the component M e of M is multiplication R e-module. Also, we prove that if R is strongly graded, then the components M g of M are multiplication R e-modules if and only if the component M e is P-torsion or P-cyclic where P is a prime ideal of the component R e of R.fatcat:azxy7xdojngjhkq5zwuzpq23qu