In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called w-operation, we show that an integral domain R is Krull if and only if for any nonzero proper w-ideal I, the Gorenstein glob...
In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called w-operation, we show that an integral domain R is Krull if and only if for any nonzero proper w-ideal I, the Gorenstein global dimension of the w-factor ring (R/I)<sub>w</sub> is zero. Further, we obtain that an integral domain R is Dedekind if and only if for any nonzero proper ideal I, the Gorenstein global dimension of the factor ring R/I is zero.