G-domains and spectral spaces

Dobbs, David E.; Fedder, Richard; Fontana, Marco

doi:10.1016/0022-4049(88)90080-1

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Theorem 161

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Cited by 4 publications

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“…Proof. Since D and D are semi normal [11], and I = I [10], On the other hand, if ∃P ∈ Spec(D) such that P / ∈ S(D), then D P is a discrete valuation ring [15]. But then,D P being a valuation domain, P D P = P implies that D P = (P : P ) and hence (P : P ) is a rank one valuation ring.…”

Section: Theorem 16mentioning

confidence: 99%

Some results on a conjecture regarding Mori domain

Gebru

2011

Math. J. Ibaraki Univ.

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Based on the famous Mori-Nagata Theorem: The integral closure of a noetherian domain is a Krull domain, similar assertion was conjectured for Mori domain as follows: The complete integral closure of a Mori domain is a Krull domain. The conjecture is positive for a noetherian domain, Krull domain, a semi normal Mori domain [6] and Mori domains for which (D : D) = 0. In general, as M. Roitman has noted [26], the conjecture is not true. In this paper, an attempt is being made, among other things, to prove that the conjecture is true for a one dimensional Mori domain and for a finite dimensional AV-Mori domain. On the other hand, using the idea of conductor ideals, a simplified proof is given that the conjecture is true for semi normal Mori domains with nonzero pseudo radical.

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Section: Theorem 16mentioning

confidence: 99%