Bass Numbers of Local Cohomology Modules with Respect to an Ideal

Let be a commutative Noetherian local ring and let be an ideal of R . We give some inequalities between the Bass numbers of an R –module and those of its local cohomology modules with respect to . As an application of these inequalities, we recover results of Delfino-Marley and Kawasaki by showing that for a minimax R -module M and for any non-negative integer i , the Bass numbers of the i th local cohomology module are finite if one of the following holds: , is a principal ideal.