A Gorenstein homological characterization of Krull domains

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 $(R/I)_{w}$ 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. KCI Citation Count: 0