Closure of Gorenstein flat modules under direct products over commutative noetherian rings

Determine whether Gorenstein flat modules over every commutative noetherian ring are closed under arbitrary direct products.

Background

The paper constructs a commutative, coherent, local, nonnoetherian ring of Krull dimension zero for which Gorenstein flat modules are not closed under direct products. The authors explicitly note that the nonnoetherian nature of this counterexample leaves unresolved the broader question for arbitrary commutative noetherian rings.

For finite stages of the constructed ring, the rings are commutative artinian and do have closure of Gorenstein flat modules under direct products. Thus the unresolved issue concerns whether the closure property holds throughout the class of commutative noetherian rings, beyond the specific noetherian settings already known to satisfy additional hypotheses such as the existence of a dualizing complex.