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Let G be a group. Let R be a commutative G-graded ring, M be a graded R-module and N be a graded R-submodule of M. In this paper, we study some cases when R is strongly graded ring and the component Ne of N is strictly non-prime, pseudo prime or pseudo irreducible Re-submodule. For example, we prove that if R is strongly graded, the components of M are multiplication and Ne is pseudo irreducible, then Ng is pseudo prime for all g ∈ G.

GRADED SUBMODULES WITH PSEUDO IRREDUCIBLE, PSEUDO PRIME AND STRICTLY NON-PRIME COMPONENTS