A generalization of the dualizing complex structure and its applications

The structural property of dualizing complex is generalized and its applications are given to show that (1) over a ring possessing a dualizing complex, the conditions of Serre on the canonical module are connected with the local cohomologies of the ring itself; (2) the Cousin complexes of certain modules over a ring possessing a dualizing complex have finitely generated cohomologies; (3) a quotient of a Cohen–Macaulay local ring which satisfies (S2) and admits canonical module, also possesses a dualizing complex.