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• W2805187941 abstract "<p>It is shown that, for all local rings (R,M), there is a canonical bijection between the set <em>DO(R)</em> of depth one minimal prime ideals ω in the completion <em>^{^}R</em> of <em>R</em> and the set <em>HO(R/Z)</em> of height one maximal ideals <em>̅M'</em> in the integral closure <em>(R/Z)'</em> of <em>R/Z</em>, where <em>Z </em>:<em>= Rad(R)</em>. Moreover, for the finite sets <strong>D</strong> := {<em>V*/V* </em>:<em>= (^{^}R/ω)'</em>, ω ∈ DO(R)} and H := {<em>V/V := (R/Z)'_{<em>̅M'</em>}, <em>̅M'</em> ∈ HO(R/Z)</em>}:</p><p>(a) The elements in <strong>D</strong> and <strong>H</strong> are discrete Noetherian valuation rings.</p><p>(b) <strong>D</strong> = {<em>^{^}V</em> ∈ <strong>H</strong>}.</p>" @default.
• W2805187941 created "2018-06-13" @default.
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• W2805187941 date "2018-06-01" @default.
• W2805187941 modified "2023-09-27" @default.
• W2805187941 title "On Nagata's Result about Height One Maximal Ideals and Depth One Minimal Prime Ideals (I)" @default.
• W2805187941 doi "https://doi.org/10.18311/jims/2018/20123" @default.
• W2805187941 hasPublicationYear "2018" @default.
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