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Integral domains having a unique Kronecker function ring. (English) Zbl 1211.13002

The paper under review has seven sections. Section 1 contains “Introduction and Preliminaries”. In Section 2 the author studies the property of having a unique Kronecker function ring for distinguished classes of domains of classical ideal theory, such as Krull domains and generalized GCD-domains. These two, for example, have a unique Kronecker function ring if and only if they are Prüfer. In Section 3 the author gives characterizations of integrally closed domains having a unique Kronecker function ring by studying their Zariski space and the integral closure of finitely generated ideals. In Section 4 the author studies pseudo-valuation domains. In Section 5 the author studies how the uniqueness of the Kronecker function ring is preserved in certain kinds of pullback diagrams. In Section 6 new examples of domains having a unique Kronecker function ring are given. Finally Section 7 is titled “Discussion and Questions”.

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13F30 Valuation rings
Full Text: DOI

References:

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