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Strongly graded rings which are Krull rings. (English) Zbl 1406.16038

Summary: Let \(R = \oplus_{n \in \mathbb{Z}}R_n\) be a strongly graded ring of type \(\mathbb{Z}\) and \(R_0\) is a prime Goldie ring. It is shown that the following three conditions are equivalent: (i) \(R_0\) is a \(\mathbb{Z}\)-invariant Krull ring, (ii) \(R\) is a Krull ring and (iii)\(R\) is a graded Krull ring. We completely describe all \(v\)-invertible \(R\)-ideals in \(Q\), where \(Q\) is a quotient ring of \(R\).

MSC:

16U20 Ore rings, multiplicative sets, Ore localization
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