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.
This paper deals with the study of behaviour of G-associated ideals and strong Krull G-associated ideals with flat base change of rings and behaviour of Gassociated ideals with short exact sequences over rings graded by finitely generated abelian group G.
We give a procedure and describe an algorithm to compute the dimension of a module over Laurent polynomial ring. We prove the cancellation theorems for projective modules and also prove the qualitative version of Laurent polynomial analogue of Horrocks' Theorem.
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