Abstract
Let [Formula: see text] be a strongly graded ring of type [Formula: see text] such that [Formula: see text] is a prime Goldie ring with its quotient ring [Formula: see text]. It is shown that the following three conditions are equivalent: (i) [Formula: see text] is a [Formula: see text]-invariant generalized Dedekind ring ([Formula: see text]-Dedekind ring for short), (ii) [Formula: see text] is a [Formula: see text]-Dedekind ring and (iii) [Formula: see text] is a graded [Formula: see text]-Dedekind ring. We describe all invertible ideals of [Formula: see text]-Dedekind rings in terms of [Formula: see text] and [Formula: see text]. We provide counterexamples of [Formula: see text]-invariant [Formula: see text]-Dedekind rings which are not [Formula: see text]-Dedekind rings.
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