We study the following properties about primary decomposition over a Noetherian ring R: (1) For finitely generated modules N ⊆ M and a given subset X = {P1, P2, . . . , Pr} ⊆ Ass(M/N), we define an X-primary component of N ( M to be an intersection Q1 ∩ Q2 ∩ · · · ∩ Qr for some Pi-primary components Qi of N ⊆ M and we study the maximal X-primary components… (More)

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