Gorenstein homomorphisms of noncommutative rings (Q1279822)

Let \(k\) be a field, \(R\) and \(S\) connected graded Noetherian \(k\)-algebras with balanced dualizing complexes. Let \(\rho\colon R\to S\) be a graded algebra homomorphism such that \(S\) has finite flat dimension as both a left and right \(R\)-module. Then the definition of a Gorenstein homomorphism is given for such a \(\rho\), and a theory for such homomorphisms is developed. ``Ascent-descent'' and ``Base-change'' results are proven, and generalizations of some classical results on Gorenstein algebras are obtained.