In this paper, we discuss a few properties of [Formula: see text]-invertible ideals over infra-Krull domains. Let [Formula: see text]-[Formula: see text] denote the multiplicative group of [Formula: see text]-invertible [Formula: see text]-fractional ideals of an integral domain [Formula: see text] and let [Formula: see text] denote the multiplicative group of principal fractional ideals of an integral domain [Formula: see text]. We proved that, if [Formula: see text] is an infra-Krull domain, then [Formula: see text]-[Formula: see text]. As an application, we can get one of Neukirch’s results directly.