Übersetzung für 'valuation ring' von Englisch nach Deutsch

valuation ring

Bewertungs­ring {m}math.

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discrete valuation ring <DVR>

diskreter Bewertungs­ring {m}math.

• But a local domain is a Dedekind ring iff it is a PID iff it is a discrete valuation ring (DVR), so the same local characterization cannot hold for PIDs: rather, one may say that the concept of a Dedekind ring is the globalization of that of a DVR.
• In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.
• Let "mw" denote the maximal ideal of "w" inside the valuation ring "Rw" of "w".
• Let "R" be a local Krull domain (e.g., a Noetherian integrally closed local domain). Then "R" is a discrete valuation ring if and only if the maximal ideal of "R" is divisorial.
• Two valuations of "K" are equivalent if and only if they have the same valuation ring.

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• is a discrete valuation ring with uniformizing parameter [...].
• One simply observes that for a discrete valuation ring "R" with fraction field "K", every "K"-point [...] of projective space comes from an "R"-point, by scaling the coordinates so that all lie in "R" and at least one is a unit in "R".
• Discrete valuation rings are equipped with a function which assign an integer to any element "r".
• Given an algebraic function field "K"/"k" of one variable, we define the notion of a "valuation ring" of "K"/"k": this is a subring "O" of "K" that contains "k" and is different from "k" and "K", and such that for any "x" in "K" we have "x"&thinsp;&isin;&thinsp;"O" or "x" -1&thinsp;&isin;&thinsp;"O".
• Other equivalent definitions use completion of a discrete valuation ring (see [...]), completion of a metric space (see [...]), or inverse limits (see [...]).

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