Dualizing Complexes over Noncommutative Local Rings

We prove an existence theorem for dualizing complexes over noncommutative noetherian complete semilocal algebras, which generalizes Van den Berghʹs existence theorem in the graded case. Using the dualizing complex, noncommutative versions of Bass theorem and the no-holes theorem are proved. We also prove that noetherian complete semilocal algebras satisfying polynomial identities are catenary.