Let M be a finitely generated module over a commutative Noetherian ring R. Then there exists a finite set {N_i|1<=i<=l} of submodules of M such that 1. intersection _(i = 1)^l N_i = 0 and intersection _(i!=i_0) N_i is not contained in N_(i_0) for all 1<=i_0<=l. 2. Each quotient M/N_i is primary for some prime P_i. 3. The P_i are all distinct for 1<=i<=l. 4. Uniqueness of the primary component N_i is equivalent to the statement that P_i does not contain P_j for any j!=i.
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