Discrete Valuation Rings and Valuations On Fields
To every field with discrete valuation we can associate the subring
of, which is a discrete valuation ring. Conversely, the valuation on a discrete valuation ring can be extended to a valuation on the quotient field giving a discrete valued field, whose associated discrete valuation ring is just .
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Famous quotes containing the words discrete, rings and/or fields:
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—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)
“You held my hand
and were instant to explain
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“And sweet it was to dream of Fatherland,
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—Alfred Tennyson (1809–1892)