Graded distributive modules (Q854597)

The authors of this paper give a characerization of graded distributive modules over a commuttive noetherian ring by proving the following main Theorem. Suppose that \(R\) is noetherian and that \(M\) is finitely generated. Let \(N\) be a graded supporting proper submodule of \(M\). Then the following statements are equivalent: (i) \(N\) is a graded distributive submodule of \(M\). (ii) For each graded submodule \(L\) of \(M\) with \(N \subsetneq L\); \(N = IL\), where \(I\) is a unique product of powers of graded maximal ideals in Supp\((M)\).