Dual of bass numbers and dualizing modules

摘要

Let R be a Noetherian ring and let C be a semidualizing R-module this paper, we impose various conditions on C to be dualizing For example, as a generalization of Xu 21, Theorem 3.2, we show that C is dualizing if and only if for an R-module M, the necessary and sufficient condition for M to be C-injective is that pi(i)(p,M) = 0 for all p is an element of Spec (R) and all i not equal ht (p), where pi(i) is the invariant dual to the Bass numbers defined by Enochs and Xu 8.