  We show that for a Noetherian ring $A$ that is $I$-adically complete for an
ideal $I$, if $A/I$ admits a dualizing complex, so does $A$. We discuss several
consequences of this result. We also consider a generalization of the notion of
dualizing complexes to infinite-dimensional rings and prove the results in this
generality. In addition, we give an alternative proof of the fact that every
excellent Henselian local ring admits a dualizing complex, using ultrapower.
