UNIQUENESS OF GRADED PRIMARY DECOMPOSITION OF MODULES GRADED OVER FINITELY GENERATED ABELIAN GROUPS

Let A be a commutative Noetherian ring which is graded by a finitely generated Abelian group G. In this article, we introduce G-graded primary submodules and G-graded P-primary submodules, and establish the uniqueness of G-graded primary decomposition. We also give a new proof on existence of G-primary decomposition.