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Three local conditions on a graded ring

Three local conditions on a graded ring

Let R = ^¡^zRi ^e a comlT>utative graded Noetherian ring with unit and let A = £fezAi '3e a finitely generated graded R module.We show that if we assume that AM is a Cohen Macaulay RM module for each maximal graded ideal M of R, then Ap is a Cohen …