Abstract
It is well known that, if A is a Noetherian integral domain, the integral closure Ā of A is not necessarily a Noetherian domain, if dim A > 2. Krull conjectured that Ā = ∩ i ∈Δ V i where any V i is a discrete valuation ring (DVR) and the intersection has finite character, i.e. if x ∈ Ā, then x is invertible in all but finitely many V i . Such a domain is called a Krull domain. Krull’s conjecture was proved in 1952 by Mori for local domains and in 1955 by Nagata in the non-local case. A proof of the Mori-Nagata theorem close to the spirit of the present paper is that given by J.Querré and based on a result of Matijévic on the global transform (cf. e.g. [32, Chapter 3]).
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Barucci, V. (2000). Mori Domains. In: Chapman, S.T., Glaz, S. (eds) Non-Noetherian Commutative Ring Theory. Mathematics and Its Applications, vol 520. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3180-4_3
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DOI: https://doi.org/10.1007/978-1-4757-3180-4_3
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