Abstract
In this paper, we construct some non-integrally closed domains in Gorenstein multiplicative ideal theory. For example, we show that there exists a Gorenstein Prüfer domain which is neither Gorenstein Dedekind nor Prüfer, and there exists a Gorenstein Krull domain which is neither Gorenstein Dedekind nor Krull. Also, we construct a non-integrally closed non-coherent domain in which all Gorenstein projective (resp., injective, flat) modules are projective (resp., injective, flat).
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